Question: Let $T^k \subseteq \mathbb{R}^n$, $ n > k$, be a smoothly embedded $k$-torus. Is its normal bundle trivial?

What about the normal bundle of $S^k \subseteq \mathbb{R}^n$, $n > k$, the $k$-sphere smoothly embedded in $\mathbb{R}^n$ (I suspect it is not always trivial)?

What I know so far: For example, I can prove that the normal bundle of $S^1 \subseteq \mathbb{R}^n$, $n > 1$, a smoothly embedded circle in $\mathbb{R}^n$, is trivial. I also know that the normal bundles of tori and spheres are always trivial in the codimension-1 case, since these manifolds are orientable. I'm interested in a more general answer.

Bigger picture: More generally, I'm interested in techniques that can be used to prove normal bundles are trivial/nontrivial.