Trapped in iPhone 4 and WhatsApp, need help to escape

You must consider two linearly independent points of this rectangle (corner or edge or middle) and investigate these point go to what points of square. Then you can find your linear transformation.

For example for part $a$ :

you must consider $4$ cases:

A) center do not lay on any axis

B) center lay on X axis

C) center lay on Y axis

D) center be $(0,0)$

and for each solve problem

Hint : you have two independent points as basis (rectangular) and T's values (that they are corresponding points on square).