How can rotation matrices be used to motivate students?

[matqkks]

I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.

 

[Ackbach]

Rotation matrices are used all over the place. They are quite straight-forward to invert, given that they are unitary transformations. In physics, rotation matrices, in effect, are used to transform from one coordinate system to another (among other transformations!).