Let q be an m x m orthogonal matrix. (a) prove that for any given vectors u and v in rm, the angle between u and v is the same as the angle between qu and qv. (b) prove that |q|2 = 1. (c) give an example 2 x 2 orthogonal matrix q, such that ||q||1 #1 and ||q|00 1 (d) prove that |qa|| = || ||2, for any mx m matrix a.