Give an example of a language $A$ that is recursively enumerable but isn't recursive, and a recursive language $B$ such that $A\cap B$ isn't recursive

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Give an example of a language $A$ that is recursively enumerable but isn't recursive, and a recursive language $B$ such that $A\cap B$ isn't recursive (if possible).

I'm a bit lost here. How do I calculate the intersection between two languages (is that the words that belong in both?)

If a language is R.E. but not recursive what that means is basically that it can fall into an endless loop?

If $A$ is non recursive and $B$ is recursive, the intersection will always be non-recursive. Correct? In that case $B$ could be any recursive language.

How do I solve this?