I am working on an assignment and am a little stuck on a question. I will try give an example without using my assignment question (hope it works!).
Given a 2 x 2 transformation matrix:
M = [-5 6]
[ 6 -5]
Q1: Write the tranformation of vector 2xi + 5yj under M
x' = [-10x + 30y]
[ 12x - 25y]
Q2: What angle has the vector above been rotated through? Explain.
So that is where I am a little stuck. I cant seem to figure this out. I tried using cos(a) = ll' + mm' (sum of the products of the direction cosines) but the algebra just blew out. Also tried the formula for the relationship between anlge and the dot product of vectors. I tried drawing and plotting lots of points. They seem to rotate a different amount depending on the initial point!!! So now I am a little out of ideas!
Any help would be greatly appreciated...