D'oh you are correct! It's a bit late here. Anyways the rest of my point stands about the author's intent. To connect that to your original comment: a rotation

D'oh you are correct! It's a bit late here. Anyways the rest of my point stands about the author's intent. To connect that to your original comment: a rotation is not "observable", instead, it's a transformation that modifies a physical system. In quantum mechanics, physical observables (energy, momentum, position, mass, etc) are always associated with Hermitian operators that act on the Hilbert space of states for the system.