insanely hard question

Question

The point (4, −9) is rotated 150? counterclockwise about the origin. Where
does it end up? Write a matrix equation to demonstrate this fact.

Answer 1

This isn't a hard problem once you understand matrix rotations.

Where [A]x[r]=[B]

[A] -is the original matrix

[r] - is the rotation matrix and

[B] -is the rotated or final matrix

 

in 2 dimensions

[r]= [cos(θ),   sin(θ)

        -sin(θ),  cos(θ)]

 

Your point (4,-9) would just be the matrix [A]= [4, -9]

 

Since counterclockwise is the positive direction you just use θ=150 in the [r] matrix and the do the cross product of [A]x[r]. The result will be the rotated location of your point (or vector).