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===== Rotation Matrices in 2 and 3 Dimensions (Lecture) =====


  - Begin with lecture/discussion: Prompted by small white board question: "What are the properties of a rotation in 2 dimensions?", students give conditions necessary for a matrix to result in rotations only. 
  - Then teacher derives the specific components of rotation (and coincidentally reflection) matrices from the condition that they preserve lengths.  Note: use lecture is a good opportunity to go back-and-forth between bra-ket language and matrices written as rows and columns of explicit components.  FIXME rewrite this lecture as a follow-up to the components activities.  Shorten!
  - Small whiteboard question: What matrix will result in a 3D rotation around the z-axis? Used volleyball to explain question. What matrix will result in a 3D rotation around the x-axis…y-axis?
  - FIXME Construction notes: Add a note and link and possibly a video clip about very small XYZ whiteboard used to help with analyzing rotation matrices in class.

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