Why is s 2(squared) the best point estimate of sigma
2 (squared)?

I will use ccw for countercloclwise and cw for clockwise for this explination.

A 270 ccw rotation is the EXACT same as a 90 cw rotation.  So to perform a 90 degree cw rotation all that has to be done is swap the x anf y coordinates and change the sign on the y.  As a general form:
(x, y) becomes (y, -x)

In your problem R is at (3, 6) so swap the 3 and 6 to get (6, 3) now change the sign on the 3 to get R' as (6, -3)