Skewering The Taylor Swift Psyops Conspiracy Babble From The Deranged Right

 

                     Travis Kelce and Taylor Swift after Chiefs win vs. Ravens

                                                                           

"Thanks to a host of right-wing news sources with a wide collective audience, everyone with half a brain (but no more) is convinced that the Democratic Party and the NFL have joined in a conspiracy to assure that the Chiefs beat the 49ers. Major right-wing media influencers, and even a one-time presidential hopeful, are uniting to spread the word of this devious plot, the purpose of which is to provide Swift an even greater platform from which to rock the 2024 vote in favor of Joe Biden...How the right will foil the plot is anyone’s guess, but they must find a way. Otherwise, Swift will entice people to vote, and if people vote, democracy is screwed.  "  Scott Ostler, SF Chronicle, today

To say Janice was devastated by her Ravens' loss to the Kansas City's Chiefs last Sunday would be an understatement.  In the parlance of Bill Russell's "Russell Report" summing up the post game malaise: 

"You look and feel like a Zombie extra on the set of The Walking Dead. The world seems surreal. Things are happening around you but you feel an out of body kind of experience. It's as if you are looking down on a catastrophic scene where pain and agony coexist. You cling to the hope it was all a bad movie you can fast forward through."  

But it wasn't a bad movie, a bad dream, or delusion. It was cold reality and Janice could barely deal with it for days on end, having fully expected the same team that thrashed the Niners some weeks ago would do the same to the pesky Chiefs and their former baseball pitcher QB Patrick Mahomes.  And that such a conquest would mean the 3rd appearance in the Super Bowl for one of the best Ravens' teams ever assembled.

But on viewing the game with her I spotted multiple early warning signs that portended disaster.  Among the first the Ravens getting the ball in the first series and going three and out. All three calls on the terrible level, no inspiration or creativity.  Then the Chiefs and Mahomes took the ball and promptly marched down the field with short 5-10 yard controlled completions, as good as runs. In 10 plays they took over 8  minutes off the clock and had 7 points. 

Why didn't the Ravens and Lamar Jackson do the same? Short, controlled, disciplined passes to take time off the clock instead of going for long bombs, holding the ball too long, taking sacks and getting picked?  Who knows?    The Ravens' D also was far from perfect, racking up 95 yards with 8 penalties.  Simply put, you can't win a game against a top tier team - especially the reigning champs - giving away almost a football field length in free yards. 

 Janice admitted all the miscues but still wondered at suspicious activity on the field. Like Chiefs' tight end Travis Kelce repeatedly escaping any penalties for offensive pass interference. "Look at that damned jerk getting away with murder!" Janice screamed.  Pop music star girl Taylor Swift was also on her mind each time the CBS' cameras flicked over to see her cheering her star boy Kelce. 

For non-football fans or those living under a rock Swift has been dating Kelce the past year or so.  What has transpired, as Lawrence O'Donnell noted in his  'The Last Word' show from last week, e.g.

 Lawrence on right-wing's Taylor Swift conspiracy: No one fuels madness like Trump (msnbc.com)

Is that Swift has effectively brought her pop mega star persona and culture into a union with the NFL via Kelce. Each time the cameras pan to see her cheering a Kelce catch or TD it resonates and reinforces the union of pop music icon and pro football heavy. It has also interjected a potent political bombshell into the never ending culture wars. To wit, the MAGA Right has now concocted a conspiracy ideation (check out Lawrence's excellent presentation in the previous ink) that the Biden Pentagon engineered a "psy ops" concatenation to ensure KC not only reached the Super Bowl, but will win it vs. SF. Whereupon when the Lombardi trophy is given, Swift will be with Kelce and announce her support for Joe Biden.

 Some may recall the 34-year-old singer endorsed President Biden in 2020, and news reports - according to the MAGAs say the White House hopes she’ll do the same this year. Screwball punk and GOP wannabe prez candidate Vivek Ramaswamy actually wrote recently on social media:

 To try to dignify his half-baked malarkey he also told the NY Times:

 “What your kind of people call ‘conspiracy theories,’ I simply call an amalgam of collective incentives hiding in plain sight.”

 To which I say, bull pocky.  It's actually an amalgam of insanity which - as Mr. O'Donnell noted - all becomes possible once people's microglia (in their brains) fall prey to horse shit.  Like the NFL has rigged all its games to ensure KC prevails and Swift and Kelce give their endorsement of Biden at the Super Bowl. The story is that the Super Bowl on Feb. 11 will be rigged so that the Chiefs win in a dramatic fashion against the Niners. Ms. Swift and Mr. Kelce will then get engaged. That way they’ll be at peak influence to cut a joint October ad for Mr. Biden.  But as Lawrence noted:

"No one ever said the Super Bowl was fixed before Trump’s madness took hold of so many people."

Ramaswamy's deranged brain spasms would be bad enough but they have also been reinforced by another nitwit, Mike Crispi, e.g.

                                                                   

This is either lunacy or it’s theater. My guess is the latter but Janice is convinced it's lunacy because the entire MAGA orbit is corrupted in its microglial cells and prey to psychotic phantasms.  Many of them spun off from the sewers of QAnon like Dems conducting Satanic rites and cannibalizing babies.  To reference Lawrence O'Donnell again, it's just a small step from believing the Pentagon and NFL are running "fake psy ops" to believing an entire political party is run by Satan and sacrifices babies.  Which is also linked up to the bollocks of "Pizzagate" that appeared before the 2016 election:

 Crackpot "Pizzagate" Tale Promoted By Michael G. Flynn Almost Led To D.C. Tragedy

True, as with Pizzagate, many of the Swift psyop purveyors well know they’re putting on an act, but there’s fame and notoriety and money to be had from spinning conspiracy ideations, the crazier the better.  The problem is that weaker- minded, lower IQ denizens (from the bottom quintiles) will swallow this swill hook, line and sinker and then someone may pay for it. Like the guy who went hunting with his rifle for Satanic child sex slaves held by Hillary at D.C.'s Comet Ping Pong  - triggered by Pizzagate.

Cut the crap and the paranoia on the right about a romance between the most popular singer in the world and an NFL player makes Republicans seem, frankly, weird as well as pathetic.  For sure, Americans who want a return to normalcy won’t find it in a movement that demonizes two of America’s healthier entertainments. Or in a presidential candidate (Donald Trump) who demonizes all those on the left including Swift - who might come out against him - and against whom he vows to settle dozens of scores if enough stupid people elect him.  Like the black students at a South Carolina college - interviewed on NBC News last Thursday night- who averred they were "excited"  because Trump "speaks his mind and shows more energy" than Biden. And you really think HE will give you all a break if elected, as opposed to putting you to work for minimum wage at one of his golf clubs?

Look, maybe the Chiefs will win the Super Bowl, or maybe not. Maybe Ms. Swift and Mr. Kelce will live happily ever after or become a pop singing duo. Who knows?  Maybe Taylor will endorse Mr. Biden again, or maybe not. Given all the death threats circulating, including by the MAGAs against judges and prosecutors who can blame her if she defaults?

But the CIA and NSA aren’t orchestrating any "fake"psy op along with the NFL and neither are the Illuminati, the Freemasons, Opus Dei, or alien lizard people (whom QAnon has tied to Dems).  Here's a question, though, for the MAGA trolls: If they truly believe defeating Traitor Trump is as easy as Joe Biden getting an endorsement from a pop singer who backed him in 2020, doesn’t that imply the Reeps have nominated the wrong candidate? 

I mean think of it! An orange fungal slimeball guilty of rape (of E. Jean Carroll) confirmed in a civil trial, as well as now facing 91 felony counts and four indictments for his massive efforts to overthrow Biden's government and who hid top secret documents. Only a moron would vote for such a useless, mindless waste of space who has also vowed to burn the constitution and turn the country into his personal dictatorship.   

Janice, meanwhile, is not assuaged by the fact the MAGA minions are all in for a Taylor Swift psy op conspiracy to ensure a KC win in SB LVIII.  As noted at the end of the Russell Report - for Ravens' fans immersed in their malaise:

"In a dastardly way, you encourage Swifties to consider Jonestown for their next vacation destination. You highly recommend the KoolAid. The meaning of life can change in this depression stage." 

But she assures me it's all based on vengeful imaginings, and more importantly   that the Chiefs lose in the Super Bowl and Mahomes and Kelce be in tears after.  That would kill two birds with one stone: 

i) balance her own pain at the Ravens' AFC championship loss with the much more significant KC SB loss, and:

ii) Spatter the Reepo idiocy that the NFL and Swift are in collusion to ensure a Chiefs' SB win.

We will see next Sunday!

See Also:

Conservatives and the Right

Fox Hosts and Ramaswamy’s Advice To Taylor Swift in Run-Up to Super Bowl LVIII: Shut Up And Sing

by Bill Berkowitz | February 2, 2024 - 7:06am | permalink

Excerpt:

Two stories are capturing the nation’s attention as we approach Super Bowl LVIII, featuring the Kansas City Chiefs and the San Francisco 49ers: Taylor Swift and the game itself!

Included in the wall-to-wall Taylor Swift coverage are: her romance with Kansas City Chief tight end Travis Kelce; her game time fashion; bets on how often CBS (the network televising the Super Bowl) will pan to Swift in the suites; and, whether, as failed presidential candidate Vivek Ramaswamy and other right wing conspiracy theorists have has speculated, the game will be fixed in favor of Kansas City so that Swift’s anticipated support of President Joe Biden’s reelection campaign will be seen as a championship endorsement.

[In late November, I posted a story about Swift’s growing political influence and whether she would endorse Biden again. Earlier this week, The New York Times ran a story headlined “Inside Biden’s Anti-Trump Battle Plan (and Where Taylor Swift Fits In.”]

The story of THE GAME ITSELF is probably of less interest to the many millions of Taylor Swift fans, and right-wing conspiracy theorists!

And:

Conservatives and the Right

Taylor Swift, Stanley Cups and a Brewing Backlash to MAGA’s Sexist Snobbery

by Amanda Marcotte | February 3, 2024 - 7:36am | permalink

— from Salon

Excerpt:

Thursday brought people who are worried about the survival of democracy welcome polling news from Quinnipiac University: For the first time in months, Joe Biden is cresting 50% in a head-to-head match-up with Donald Trump. That puts the current president 6 points ahead of the former president, who had been enjoying an alarming lead in polls for months, despite being under 91 felony indictments in four separate jurisdictions. We have women to thank for this swing towards basic sense and decency in the polls.

"Women 58 - 36 percent support Biden, up from December when it was 53 - 41 percent," explains the Quinnipiac analysis. "Men 53 - 42 percent support Trump, largely unchanged from December when it was 51 - 41 percent."

So you enjoy bashing Taylor Swift, Republicans? Well, how's that working out for you?

And:

Donald Trump

Americans, Dead Inside, Can Still Feel Trump

by Phil Wilson | February 3, 2024 - 6:06am | permalink

Excerpt:

Trump barely exists outside of our imaginations. Our minds have constructed him from the detritus of America's decay. If we are dead inside and feel nothing, we can still feel Trump. Trump's putrid face is America's feeble pulse.

What have we done to deserve having the world's ugliest infection decomposing inside of us? You can't kill it with antibiotics, can't severe its grip with the rusty blade of politics, or scrape it off with a chunk of coarse sand paper. Even if you could, it would grow right back like fungus on a dead log. How many of us have had the dream—either awake or asleep—of stabbing it with a sword, tossing it overboard into a whirlpool of famished sharks, or clubbing it with a Louisville Slugger until it has been reduced to a puddle of raw sewage. Have a hundred million people savored this same fantasy? No! It has to be more, way more, and that is the point—no amount of collective outrage has any use. The terrible malignancy gets bigger as if the gathering ire nourishes it with fresh methane-infused wastewater.

Solutions to (Mensa) Brain Buster Challenge (#3)

1) Arrange the 6 L-shaped pieces above into a 4 x 6 grid such that:

- Each row has the same number of stars

-  Each column has the same number of stars.

- No diagonal has 4 stars.

The pieces may be rotated but not reflected.

Solution:   The best approach is to cut the pieces out  and assemble them  - according to the rules - like  a jigsaw puzzle, to get;

2) Prove all square numbers (1,4,9,16, 25...) are either divisible by three OR have a remainder of one when divided by three.

Solution:  All numbers, including square numbers, are a multiple of 3 (or 3n). Or a one more than a multiple of 3, i.e. (3n + 1), or one less than a multiple of three, i.e. (3n - 1).   Then:

(3 n) ²   =   9 n ²   =   3 (3 n) ²   is divisible by 3

While:

 (3 n + 1  ) ²    =   9n ² +   6n +   1 =   3 (3 n ²  +   2n) + 1

has a remainder of 1 when divided by 3.

Lastly:

 (3 n -  1  ) ²   =   9n ² -   6n +   1   =   3 (3 n ² -   2n) + 1

has a remainder of 1 when divided by 3.

3) Find all solutions for positive integers a and b (a > 1):

(a + 2)! a! (a - 2)! = b!

Then prove there are no other solutions.

Solution:

There are two solutions:  a = 3, b = 6

I.e.  (a + 2)! a! (a - 2)! = b!

=  (3 + 2)! 3! (3 - 2)! = 6!  =   5! 3! (1!) = (5 x 4 x 3 x 2 x1) (1) (3 x 2 x 1)

=  120 (6) = 720

Also:   a = 5,  b = 10

=  (5 + 2)! 10! (5 - 2)! = 7!  5! 3!  =  362, 880

We prove there are no solutions for a > 6:

4) Given a rectangle of length  (Ö2) x  and height x, we have one circle and two semi-circles inscribed within it,  and all three intersect at two points, as shown below:

Find the area of either green crescent shape between the two arcs in terms of x. 

Solution:

We render the sketch so it conforms to:

Where u and v mark the end points where the circle and both semi-circles intersect. Then line segment uv is a diameter of the inscribed circle.   We then let w (extreme mid point of bottom line of rectangle)  be the point where the inscribed circle is tangent for the bottom side of the rectangle, which is also the diameter of the lower semi-circle.  

Note than an inscribed angle subtended by a diameter is a right angle.  Therefore, angle uvw  is a right angle.  Further,  line segment wv is a radius of the lower semi-circle, i.e.

wv =  ½(Ö2p) x

And line segment uv is the hypotenuse of right triangle uvw, so:

uv = 1/2 (Ö2) (Ö2) x  = x 

The area of the inscribed circle is then:

A(c)= p (x/2) ²   =  (p /4) x ²

The area of the upper half of the inscribed circle is:

A(c1) = (p /8) x ²

The area of sector uwv of the lower semicircle is:

A(uwv) =  (p /4) [½ (Ö2)x]²  =  (p /8)x ²

The area of the chord uv of the lower semicircle is equal to the area of the sector uwv minus the area of the right triangle uwv:

A(uv^) = A(uwv)  -  A(<uwv) =

 (p /8) x ²   -  ½ [½ (Ö2)x] [½(Ö2)x] = (p /8)x ²  - (¼) x ²

The area of the lune then is equal to the area of the upper half of the inscribed circle minus the area of the chord uv,

A(L) = A(c1)  -  A(uv^)  = (p /8)x ²  - [(p /8)x ²  - (¼) x ²]

A(L) = (p /8)x ²  - (p /8)x ² + (¼) x ²  =   x ²/4

5) We are given the equation:

A^B + C^D = E ^F + G^H + I^J + K^L

 

We obtain on appropriate replacement of letters A-L with integers 0-11:

11⁰ + 5⁶ = 0 ⁷ + 2⁸ + 9³ + 11⁴

And:

1⁷ + 5⁶ = 0 ¹⁰ + 2⁸ + 9³ + 11⁴

 

Of which there are 96 total permutations.

There are in addition 96 total permutations for:

1⁹ + 4⁷ = 0¹⁰ + 2¹¹ + 3⁸ + 6⁵

And:

1¹⁰ + 4⁷ = 0⁹ + 2¹¹ + 3⁸ + 6⁵

 

There are in addition 96 further total permutations for:

3⁹ + 7² = 0¹⁰ + 5⁶  + 11¹ + 8⁴

And:

3⁹ + 7²  =  11⁰ + 5⁶ + 10¹ + 8⁴

 

Yielding a total of: 96 + 96 + 96 = 288 answers/solutions

 

Solutions To Brain Busters #2 ('Math Maulers)

1) (a) If (3x + 1)/3 - (x - 3)/2 = 2 + (2x - 3)/3

find the value of x:

We begin by simplifying both sides and obtained lowest common denominator:

-> (6x + 2 - 3x + 9)/ 6 = (6 + 2x -3)/3 = 2(2x + 3)/6

-> 6x + 2 - 3x + 9 = 4x + 6

-> 3x + 11 = 4x + 6

-> x = 11 - 6 = 5

Which can be inserted into the original (fractional) equation to verify both sides are equal.

(b)b) Factorize completely:

(i) 15 x ^y - 20 xy²

= 5xy (3 - 4y)


(ii) 3 - 12b ²

= 3 (1 - 4b ²) = 3 (1 - 2b)(1 + 2b)

(c) Given that: m = -3, n = 2, p = -1

find the value of:

m(p - n) ²/  3p + m

Substituting:

-3(-1 -2)²/ [3(-1) + (-3)]

= -3(-3)²/ [-3 + (-3)] = -3(9)/ -6 = 27/6 = 9/2

2) f and g are functions defined as follows:

f: x -> 3x - 5

g: x -> x/2

a) Calculate the value of f(-3)

f(-3) = 3(-3) - 5 = -9 -5 = -14

b) Write expressions for (i) f^-1(x) and (ii) g^-1(x)

(i)the inverse function is obtained by exchanging x and y places and solving for the other variable, viz: x = 3y - 5, then y = (x + 5)/3, therefore:

 f ^-1(x)   = (x + 5)/3

(ii) Similarly, g^-1(x) = 2x (since x = y/2 and hence y = 2x)

c) Hence or otherwise, write an expression for (gf)^-1

This is a composite function of the first two, with the order of priority in operation to the right, e.g.  f ^-1 first then  gf^-1. Hence, combining the two:

(gf)^-1 = 2 [(x + 5)/3] = 2/3(x + 5) or 2x/3 + 10

3) From inspection of the graphs (above), the coordinates of the points L and N are (5, 6) and (8, -2), respectively.

(i)State the coordinates of the midpoint M of the line, LN.

This can easily be done by visual estimation, since we know the endpoints of the line. The midpoint M will be displaced from the L,M positions by half of each of the (x1,y1) coordinates, or: x1 + ½ dx, y1 + ½ dy, where dx = 3 (e.g. 8 - 5), and dy = -8 (e.g. -2 -(6)). . Thence: x + ½ dx = 5 + 1.5 = 6.5 and y2 + ½ dy = 6 + (-8)/2= 6 -4 = 2. Then, M is located at (6.5, 2).

(ii) Calculate the gradient of the line LN

The gradient is defined: (y2 - y1)/ (x2 - x1) = (-2 -6)/(8 - 5) = -8/3

(iii) Determine the equation of the straight line which is perpendicular to LN and which passes through point M.

We already have the coordinates of M, so this straight line must pass through them, hence we can use the point slope form for a straight line, viz.

y - y1 = m (x - x1) to find this line, while realizing that if it is perpendicular to the existing line, then the slope (gradient) must be the inverse, or 3/8 (not -8/3)

By the point slope formula:

y - 2 = 3/8(x - 6.5) = 3/8(x - 13/2)

y - 2 = 3x/8 - 39/16, or:

y = 3x/8 - 39/16 + 32/16 = 3x/8 - 7/16

This line is shown for clarity in the accompanying graph above (though it does not have to be given as part of any solution.)

b) An aircraft leaves Jamaica at 13:55 hrs. and travels to Barbados via Antigua. The average speed of the aircraft is 420 km/hr. It arrives in Antigua at 16:45 hrs. local time. Given Antigua is ONE hour AHEAD of Jamaica, compute the distance.

The total time as given is 2 hrs. 50 mins. (16:45 - 13:55), but one must correct for the difference in time zones (1 hr.). Hence, the actual time of flight is:

2 hrs. 50 mins. - 1hr. = 1hr 50 mins.

Then the distance covered will be 420 km (for one hour) plus the extra distance covered in the 50 mins. or 50/60(420 km) = 350 km. Therefore, the distance covered is:

420 km + 350 km = 770 km

(4) (a) Calculate the exact values of:

i) (2.8 + 1.36)/ 4 - 2.7

This is: 3.2

ii) (27/8)^1/3

Here we recognize two cube roots, so:

a) (27/8)^1/3 = 3/2 = 1.5

b) Calculate 9.72 x 12.05

i) Exactly

This is: 117.126

ii) Correct to two decimal places

This is: 117.12

iii) Correct to 2 significant figures

This is: 110

iv) In standard form

This is 1.17126 x 10² (using the exact form translated to standard which is always the number N x 10ⁿ where n is the exponent to which 10 is raised)

5)Using Fig. 1 from original post(see above)  and the information therein, calculate (giving reasons):
a) Angle MSQ

The key to the solution lies in recognizing the presence of the similar triangles: SRM (to SRP), and SQR (to SPQ). Once these are in place, and also using the results for supplemental angles one can find all the angles given. Thus angle MSQ = 24 deg.

b)Angle RSP

By similar triangles (SQR and SPQ): < RSP = (78 - 26)deg = 52 deg

c)Angle SPN

By similar triangles(SMQ and PQN), alternate interior angles being equal, and working therefrom: angle SPN = 102 deg.

6)(a) Given that: U = {a, b, c, d, e, f, g} where U is the universal set, and

L = {a, b, c, d, e}

M= {a, c, e, g}

N = {b, e, f, g}

(i)Draw a Venn diagram showing the sets U, L, M, N and their elements

The solution to this is shown in the accompanying image:

ii) List the members of the set represented by the union of N with the intersection of L and M

From the Venn diagram solution in (a) we obtain: {a, b, c, e, f, g}

b) If:

(a)
(b) =

(2...3)(-3)
(-1..2)(1)

determine the values of a and b

This is done by simple matrix multiplication, i.e. multiplying the 2 x 2 matrix on the left side by the column matrix on the right. We get:

(2 x (-3) + 3 x 1)
(-3 x -1 + 2 x 1) =

(-6 + 3)
(3 + 2) =

(-3)
(5)

so that a = -3 and b = 5

c) Given the vector:

A =

(4)
(7)

Calculate:

i) ‖A‖, the length of vector A

This is simply: A = [4 + 7²]^1/2 = [65]^1/2 = 8.06

ii) The size of the angle made by the vector A and the x-axis.

We need to recognize here that the tangent of the angle is 7/4 since tan Θ = y/x and for A, x = 4 and y = 7. Then: Θ = arctan (y/x) = arctan (7/4) = arctan(1.75) and thence, Θ = 60. 2 degrees.

7)The diagram (Fig. 2) represents the Earth and shows the equator and the Greenwich meridian. Town I is located at (16 N, 30 W), and Town J is at (16 N, 45 W).

(i) Copy the diagram (or print it out) and show the positions of Towns I, J.

The solution for this part is provided in the graphic referenced to Problem (7). The key point is to note that town I must be closer to the Greenwich meridian (at 0 degrees longitude) and town J 15 degrees further to the west. Both are on the same latitude circle 16 degrees north of the equator (0 degrees latitude).


(ii) Calculate the radius of the circle of latitude on which Towns I and J are situated.

From simple solid geometry one can show that the radius (r') of 16N latitude circle is reduced by a factor equal to the cosine of the latitude, or 16 degrees. This should be evident from inspection of the same solution diagram, from which we can ascertain: cos (16 deg) = r'/r where r is given as 6400 km. Therefore:

r' = r (cos 16) = 6400 km (0.96) = 6150 km.

(iii) Calculate the shortest distance, measured along the Earth's surface, between the two towns.

This would be along the latitude circle of 16 degrees N, which separated the towns by 45 - 30 = 15 degrees. So the distance will be the fraction of this separation over 360 degrees, multiplied by the circumference for the 16 N latitude circle. Call the latter C(16N) and C(16N) = 2π (r') = 2π (6150 km) = 2(3.14)(6150km) = 38620 km

Then: d (I-J) = 15/ 360 (38620 km) = 1, 600km

8)The matrix R =

(cos(Θ)......-sin(Θ))
(sin (Θ)......cos(Θ))

a) Determine the coordinates of the image (1, 2) under the transformation R when Θ = 90 degrees.

This is done via simple matrix multiplication and when substituting for Θ in the R-transformation matrix (e.g. Θ = 90) we find, 

R(1 2) =

(0...-1)(1)
(1....0)(2) = (-2 ...1)


b) If the point (p, 3) is on the line (L)given by: x + 2y = 5, calculate the value of p.

This is straightforward. We have x = p and y = 3, so p + 2(3) = 5, and p = 5 -6 = -1.

c) Given the point (1,2) is on L, determine the image of L (L') of the line L under the transformation R.

This is more involved but we already know from part (a) how the image of the point is produced via the R-transformation matrix. Since: R(1 2) = (-2 1) and y = -x/2 + 5/2 then we can use the point slope formula: y - y1 = m(x - x1) to obtain the new line which is really L' the image of L:

Then: y - 1 = -½ (x - (-2)) = -x/2 + 2 or y = -x/2 + 3 

or (re-arranging):

x = 2y -6 or x - 2y = -6

d) Write the matrix equation to represent the pair of simultaneous equations given by L and L'.

This is straightforward since we know the two equations are: x + 2y = 5 and x - 2y = -6. Then:

(1...2)(x)
(1..-2)(y) =

(5)
(-6)

9) This refers to Fig. 3 from the original post.

The diagram shows a rectangular sheet of metal ABCD supported by a vertical wall (shaded) at right angles to the level ground OX. AB measures 3 meters and AD measures 10 meters.

a) Calculate the size of the angle ODA.

From the geometry we recognize that sin (ODA) = opp./hyp. = OA/ AD = 4/10. Then:

angle ODA = arc sin (0.4) = 23.5 degrees.

b) Hence, calculate the size of the angle CDX.

From inspection and basic knowledge of geometry (i.e. the contributions to a straight angle must total 180 degrees) we see:

angle CDX = 180 deg - (90 deg + 23.5 deg) = 180 deg - 113.5 deg = 66.5 deg.

c) If CX represents the length in meters of C above the ground, calculate CX.

We use, after noting the geometrical relations:

sin (66.5) = CX/ CD, but CD = AB = 3m, (by def.) so sin(66.5) = CX/ 3 m

CX = 3 m (sin 66.5) = 2.75m

10)This refers to the Venn diagram in Fig. 4 in original post, and the information therein. 

Assume the same number, x, play football only and tennis only.

(a) Calculate the number who play football.

From the Venn diagram and relations shown therein, we have:

U = 40 = F + C + T + 8

and F + T = 2x (x = those who only play football, and tennis). 

From the diagram we also see those who play cricket C = 15, so:

F + T = 32 - C = 32 - 15 = 17. (This number refers to those who play both football and tennis). Since the intersection of F and T shows '7' then it follows that:

2x + 7 = 17, and 2x = 10, with x = 5 is the number who play football only and tennis only.

 But the number that play football must logically include not only those who play football only but those who play football PLUS tennis, as well as those who play cricket plus football, hence the answer is: 7 + 15 + 5 = 27. To check this, add to this those who play only tennis (5) plus those who play neither football, tennis or cricket (8) and you obtain: 27 + 8 + 5 = 40, the total of members.

(b) State the information represented by the shaded portion of the Venn diagram.

This refers to the numbers that play both football and tennis.

(c)State the relationship between the members of the sets C and F, and between the sets C and T.

In the first case, since C is a subset of F, then all the cricketers also play football, however in the second case, the result is the empty set since there is a disjoint relation between C and T.

Solutions To Brain Busters #1 ('Logical Labyrinth')

 (1) We already know C is at zero degrees Celsius (O C) so all we have to do is correctly compute the total difference in temp. to object O. This is just: dT = 2F + 1.8C . Thus, we know O is at a temperature of more than 1.8C. Now how many C degrees in 2F? The hint provides the basis for deducing the answer (if one didn't already know it) so 1 C = 1.8F 

Then logically, 2F = 1C + 0.2F, and for 0.2F: 

0.2F/ (1.8 F/C) = 1/9 of a Celsius degree = 0.11 C

Therefore, 2F = 1.11 C

So O is at a temperature of: 1.11C + 1.80 C = 2.91 C 

Which is answer (C)

(2) This is straightforward. Obviously, a consecutive clockwise and counter-clockwise rotation of 60 degrees cancel each other. Then, rotating the triangle through 360 degrees clockwise simply turns it through a full circle - bringing it to its original position. Thus, the answer is: (A) the same as the original orientation.


(3) We know A and B choices are immediate conditions based on the information. Since we already have more than one choice, the answer has to be (D) - all the preceding may apply.

(4) A straightforward logical regression and deduction exercise:   (D)

(5) We have consecutive operations such that: operations: addition by 1 is denoted by A; multiplication by 2 is denoted by S; division by 4 is denoted by F, and subtraction by 1 is denoted by T.

Then: 28 SFATS -> (28)x 2 = 56 and 56/4 = 14 and (14 + 1) = 15 and (15 - 1) = 14 and finally 14 x 2 = 28

So the answer is: (B)

(6) This references a series of operations on a square whose top left corner is A, and the other corners (going clockwise) are: B, C and D. The operation sequence is: R2 M1 M3, where,

R2: rotation clockwise by 180 degrees

M1: Mirrors corners exactly through the midline of the square

M3: Mirrors two opposing corners in the opposite sense to M2

Now, performing operation R2 first, causes the square to rotate so that 'A' ends up where C is in the original orientation. (Fig. 1(A)) Operation M1 then causes all the existing corners to be mirrored through the midline of the square. Thus, Fig 1 (B) shows the orientation after M1.

The last operation, M3, mirrors two opposing diagonal corners: from top right to bottom left (e.g. opposite to the sense of M2) This will yield the result shown in Fig. 2 which is DABC or (C). 

(7) The key is to carefully read the conditions proposed for affecting the rate of synthesis, and to note that the density of the proteins will have nothing to do with this rate. All "an increased density of the proteins" means is that more will be there to be synthesized but this doesn't affect the rate applied to each of the proteins proper. (Of course the total time to complete the task will be longer but this is only because there will be 1000 times more to be synthesized!) Thus, galactoside at half the original concentration means the rate of synthesis slows by a factor of two, so we can expect only 500 molecules (as opposed to one thousand) to be synthesized for every five generations. Thus, the answer is: (B). 

(8) The next step in the sequence is easy to figure out once one identified the key components of the previous sequence of 4 and how they are changing. This is in the direction of increasing white squares and reducing the orange. Since the algorithmic sequence requires at least two whites for the next step, this automatically eliminates options (A), (C) and (D), leaving answer (B). 

(9) The key for this question's response is not to be fooled by the 'easy pop-up answer' which is (D). Clearly, on careful reading he has invented an  ad hoc law to permit miracles and that contradicts laws of logic and the general law.   The key sentences that give it away?  "A miracle is an exception to physical law but not to logical or ethical law. As such it does not contradict the general law "

BUT - if it contradicts the physical law, it also contradicts the general law- by his own definition.

Hence, answer is (C).

(10) In the case of this answer, the conclusion allows for a multiple points of view and this definitely prescribes answer (D): He has committed all the above.

(11) Ditto with respect to the author's reference to a "general law", i.e. he's committed all the following logical errors:

i) He has conflated "general law" with laws of thought, without defining the former.

ii) He has committed the "one True Scotsman" fallacy, i.e. asserting a certain association always trumps any other associations by virtue of having some special dispensation or quality (usually an appeal to "authority" or an undefined God).

iii) He has erred in extrapolating from the particular to the general.