. The new basis vectors can be
expressed in terms of the original Cartesian basis 
as
and 
.Given:
A new basis . The new basis vectors can be
expressed in terms of the original Cartesian basis as
and .
Asked:
Find (1) the change of basis matrix P from E to S;
(2) the change of basis matrix Q from S to E;
(3) the components (a',b') of an arbitrary vector 
in
the S basis if has components (a,b) in the Cartesian
coordinate system (
.)