$18\mathrm{.}33$ The coordinate axes shown represent the principal centroidal axes of inertia of a $1500-kg$ space probe whose radii of gyration are $k_x=0\mathrm{.}4m,k_y=0\mathrm{.}45m,$ and $k_z=0\mathrm{.}375m.$ The probe has no angular velocity when a $150-g$ meteorite strikes one of its solar panels at point A with a velocity $v_0=(720\frac{m}{s})i-(900\frac{m}{s})j+(960\frac{m}{s})k$ relative to the probe. Knowing that the meteorite emerges on the other side of the panel with no change in the direction of its velocity, but with a speed reduced by $20$ percent, determine the final angular velocity of the probe.