I want to use k2 with joomla standard modul like "Articles Category" but i don't see Category from k2.
Image:
http://gyazo.com/3c7659e5242f816ae5ee336321b594f8

You have to use the K2 Content module instead, if you want to display K2 items, and the K2 Tools module if you want to display categories.

You cannot however display com_content articles/ categories and K2 content in the same module.

But i need to use standard module from joomla because i want to change theme and for this new theme need use standard module and standard module not have k2

Theme: www.joomlart.com/demo/#ja_playmag
Documentation: www.joomlart.com/documentation/joomla-templates/ja-playmag

You have to ask Joomlart if they have that template for the K2 Content module.
Joomla modules only suppor the default articles.