A thin, flat uniform metal triangle lies in the x-y plane with its corners at (1,0,0),(0,1,0), and the origin. Its surface density (mass/area) is ρ = 24. (Distances and masses are measured in unspecified units, and the number 24 was chosen to make the answer come out nicely.)
(a) Find the triangle's inertia tensor I.
(b) What are its principal moments and the corresponding axes?