A = 4 2

-5 -2

Im suppose to find an invertible 2x2 matrix Q such that Q^-1AQ is equal to a rotation followed by scaling a positive real number, and write down both the rotation matrix and the scaling matrix. Also, what is the angle of the rotation matrix?

When I do the work I get

Q^-1AQ = -5 1

-37 7

I'm not sure if this is correct and if it is, I dont know how to find the scaling and rotation matrix