Let Q be an orthogonal matrix, and I want to transform (p,q), the magnitude of this vector is sqrt(p^2+q^2) using pythag. T((p,q))=pv1+qv_2 where v1 and v2 are the column vectors of Q. Since the column vectors of Q have magnitude of 1, this means pv1 has magnitude of p and qv2 has magnitude of...