Draw vector in the plane.

Form a parallelogram to draw .

Now, let be rotated by - draw it.

Now, let be rotated by - draw it.

And let be the vector rotated by - draw it.

Argue that by looking at it geometrically.

is the point rotated by . Therefore, .2) Compute given

is the point rotated by . Therefore, .

Now you should be able to form the matrix.

Remember that where is angle between them. But have the same length and the same angle between themselves because is rotating both of them by the same number of degrees. Thus, .3) Consider the standard inner product <u,v> on . Show that it is invariant under the transformation T.