Hint 4

By symmetry, the principal axes of the brick are parallel to edges. You should take these as your coordinate axes. The principal moments are just the moments of inertia about these axes and can be calculated as in Question 3, part (a) on Examples 4.

The angular velocity is

$$\hbox{\boldmath $\omega$}={\omega\over\sqrt 6}(1,\ 1,\ 2)$$

Acting on this with the moment of inertia tensor gives

$${\bf L}={Ma^2\omega\over 12\sqrt 6}(5, 5, 4)$$

The torque required is

$$\hbox{\boldmath $\tau$}={Ma^2\omega^2\over 12}(-1,\ 1,\ 0)$$