did the commands above the problem still persists.
my ubuntu is under the proxy

W: GPG error: http://archive.ubuntu.com precise-updates Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>
W: GPG error: http://archive.ubuntu.com precise-backports Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>
W: GPG error: http://archive.ubuntu.com precise-security Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <ftpmaster@ubuntu.com>
W: Failed to fetch http://archive.canonical.com/ubuntu/...amd64/Packages 404 Not Found


I imported key and tried to update this like apt-gey update, but still no luck