Following is a graph that contains both coordinate systems (x,y) and (x',y'). x, y, x', and y' are all axes
y'
^
|
+----------> x
| | | |
+--+--+--+
| | | |
+--+--+--+
| | | |
+--+--+--+-> x'
|
v
y
Above is a picture of a graph. For example, the following is graph or grid of the (x',y') coordinate system.
y'
^
|
+--------+
| | | |
+--+--+--+
| | | |
+--+--+--+
| | | |
+--+--+--+-> x'
What is the transformation T which transforms coordinates (x,y) to coordinates (x',y')? Please include simple, intuitive explanations and steps. Note: the solution, T, is probably a 2d matrix.