  We use a generalized Gross-Pitaevskii equation for the condensate and a
semi-classical kinetic equation for the noncondensate atoms to discuss the
scissors mode in a trapped Bose-condensed gas at finite temperatures. Both
equations include the effect of $C_{12}$ collisions between the condensate and
noncondensate atoms. We solve the coupled moment equations describing
oscillations of the quadrupole moments of the condensate and noncondensate
components to find the collective mode frequencies and collisional damping
rates as a function of temperature. Our calculations extend those of
Gu\'ery-Odelin and Stringari at T=0 and in the normal phase. They complement
the numerical results of Jackson and Zaremba, although Landau damping is left
out of our approach. Our results are also used to calculate the quadrupole
response function, which is related to the moment of inertia. It is shown
explicitly that the moment of inertia of a trapped Bose gas at finite
temperatures involves a sum of an irrotational component from the condensate
and a rotational component from the thermal cloud atoms.
