Hi all,

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

My answer...

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...