Sets and ordinals - homework questions

Question

I have two questions which I don't even know how to start. I would like you to give some hints. I know it would be better that I show some work, but I really don't know where to begin...

The question goes like that:

Find whether the sets are isomorphic and whether the order types are equal.

1. $\omega\cdot{\omega}$ and $\omega+\omega$ where $\omega$ is the first infinite ordinal.
2. $q+1+q$ and $q\cdot{q}$ where q is the order type of $(\mathbb{Q},\leq)$.

Please help, thank you!

Answer 1

HINTS:

1. Note that there is just one limit ordinal smaller than $\omega+\omega$.
2. Only one of these orders is dense. Two countable dense orders with the same endpoints are isomorphic. (Thank you bof for the correction.)