`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.