Will someone help me with this problem about linear transformation. Let defined to be the transformation of rotation of the plane by angle around 0.

1) Show that T is linear.

2) Compute given

3) Consider the standard inner product <u,v> on . Show that it is invariant under the transformation T.

For part 1) I tried to formulate T after drawing the picture I have something like , here then I rewrite this in term of , but my professor told me this is not how he wants it. He wants me to draw some paralellogram and do it like a geometric proof, which I have no idea. I tried to formulate this because I want to show T(cx+y)=cT(x)+T(y).

For part 2) he also wants me to do it geometrically. I really don't know how to di it. Can someone help please?