Rotations after swapping axes

I have a model parsed from a Collada file, and it was arranged weirdly so I have to rotate it -90 degrees on the x-axis so it is on the ground facing the front.

I have figured out that this means the z axis becomes what used to be the y axis, and the z axis becomes what used to the be negative y axis. I use this in calculating the centre of the model.

Now I want to put some random rotations on the model, and I need to work out what each direction of rotation becomes. For example, does a rotation on the y axis become the rotation on the z axis?

I guessed that I could just swap the y and z rotations but it didn't work. I also tried making either or both of them negative and that didn't help. It's really hard to figure it out on paper!

If someone can give me an answer that would be awesome! Or direct me to a good link on linear algebra :-(