No, but you can multitask just like on any Android phone or the iPad where you can switch between applications with a single button.
Thank you for the question!
However, I have one more. I have seen, that in the tablet Samsung Note 10.1, when watching any video, that "window" can be reduced (something like that), and you can do something other what you want to, like chatting while watching a video. If it possible to do such things on Nexus 10?
If one Samsung's Android tablet is able to do this, then I don't see any reason why the other Samsung's Android tablet should not be able to do the same. Unless it's vanilla Nexus. Vanilla Android has no OEM-specific interfaces or built-in's, it is plain naked Google's Android.
So, if you want to have mentioned Samsung's multi-window functionality, you need to go for Samsung non-Nexus tablet. Otherwise - wait until Google implements something similar.
Closest thing to what you're wanting that I can think of would be widgets. Could potentially fill a page with the widgets of apps that you'd like to multitask with.