Suppose we are given the unit square A in the plane with corners (0; 0), (1; 0), (1; 1) and (0; 1). (a) Find a linear transformation T that sends A to the parallelogram B with corners (0; 0), (1; 2), (2; 2) and (1; 0). (b) Is the linear transformation T unique? Why or why not? (c) What linear transformation S, other than the identity, would send A to itself? (d) Is there a linear transformation whose overall e ect would be to send A to B and then translate B in the horizontal direction by one unit? Explain. (e) Find a linear transformation that will send A to a parallelogram C of area 4 while still keeping (0; 0) and (1; 0) as two of its corners. (f) What is the general formula for the linear transformation that sends A to a parallelogram of area k while still keeping (0; 0) and (1; 0) as two of its corners?