Transformation between 2D coordinate systems

Question

Let there be two coordinate systems:

1. unit coordinates at $(0,0)$, rotated by 45 degrees
2. the same, but at $(5,5)$

How would I go about to create a transformation to convert #2 coordinates into #1 coordinates?

Is it possible by multiplying standard geometric transformations, i.e. translate, scale, rotate?

Answer 1

You know the transformations for rotation by 45 degrees, for translation by (5, 5), and for rotation by 45 degrees back again. Compose them to get the answer!