two axes on top of one another with one rotated

​Sorry if this ultimately goes through more than once. I am having some issues with submitting it…

I need to teach coordinate systems and transformations to a college robotics class. I have used Tikz in the past to generate some graphics,
but I want to switch to doing everything in matplotlib if possible. (Tikz is super powerful and makes beautiful graphics, but it always takes me a long time to generate a figure).

One of my initial problems is drawing two axes on top of one another, but with one of them
rotated by an arbitrary angle. I am attaching the Tikz result that I want to recreate in matplotlib. Other than drawing lines “by hand”, I don’t really know where to start. Any help would be appreciated.

In case the mailing list doesn’t allow attached graphics, here is a link to the image
on my google drive: