sudo cp -rp /home/my_home /media/backup/my_home

From cp manpage:

 -p     same as --preserve=mode,ownership,timestamps

 --preserve[=ATTR_LIST]
          preserve the specified attributes (default: mode,ownership,timestamps),
          if possible additional attributes: context, links, xattr, all

What you want is:

cp -R t1/. t2/

The dot at the end tells it to copy the contents of the current directory, not the directory itself. This method also includes hidden files and folders.