 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2017/8/b/i/solution

In the quadratic form, the two equal off-diagonal contributions together supply the mixed term. Comparing coefficients gives

M = I_{0} (2 - 1 - 1 2) .

For a nontrivial physical moment of inertia scale take

I_{0} > 0

; then this inertia tensor is positive definite.

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