`I'm having some trouble on this one: consider the set V of all polynomials of degree 2 or less, and let $\langle u, v \rangle = \int_0^1 \! p(x) \!q(x) \, \mathrm{d} x$
Find a matrix A such that $\langle u, v \rangle = u^\top Av$ and find an orthonormal basis of V with respect to this inner product.