bad beagle is destroying my carpet

I'd be using a crate when you go to work.

Welcome to i-dog!  I love beagles (I have a beagle mix).  My next dog (far, far in the future) is gonna be a pure breed beagle.
 
Hope you can work out your potty problems.  My pup was crate trained while in rescue (I adopted her at 14 weeks) and she was crated for a number of months when we couldn't have "eyes on" her.  She only had two accidents.  I think crate training is great!  Good luck!

I agree with the others suggestion of crating her when your out.
A bored beagle can be very destructive - trust me, I've been there.
 
Buster, our beagle actually dug up the carpet when he was a pup.
But when he dug a hole thru the wall, clear thru the sheet rock, I had
to do something. At about 1.5 yrs.old he had put 1 hole in 3 different
walls - that is just crazy.  
 
Crate training he is the best for him & our house. Just like any other
command, sit, stay, etc... he knows "go inside" and he happily goes
inside so that he will get rewarded.

I would also suggest using a hard crate, not one of the soft ones.  Of course I could never be speaking from experience because my dear sweet dog would never do anything destructive (Miss Sydney, not naming any names) it isn't fun coming home to a hole in the crate all the way through to the carpet and then moving the crate and finding that the huge lump of yarn that was in the crate that you couldn't figure out where it came from, came from the carpet underneath that apparently needed to be unraveled.

You also need to be using an enzyme cleaner such as Petastic on the carpet, which will help get rid of the odor.  If the dog can smell it, he will keep going back to the same area.

I think she does it just to show me shes mad that I left

 
Dogs don't do potty as a means of punishing us!  What she is showing you is that she has to go potty and she doesn't know how to properly ask to go outside AND she's afraid to do it right in front of you.  This is why you can walk out of the room for a minute and when you return, she's gone potty!  She's *waiting* for you to leave the room so she can go.  Please don't correct her or do anything crazy like yell at her or (the absolute worst) rub her nose in it.  
 
You have 2 issues here - 1. She's not fully potty trained and 2. She's afraid to do potty in front of you (which could easily be slowing down #1!!)   You need to go back to potty training 101 and crate her when you are gone.  As soon as you return, take her directly outside and throw a freaking party when she eliminates outdoors.  She needs to learn that you LOVE it when she goes potty and she'll relax a bit and stop trying to *hide it* from you. 
 
Who knows what she learned in her previous home.  She may think that she is not allowed to go in front of you.   Seriously, every time she goes outside - give her treats and tell what a GOOD GIRL she is, give her kisses and hugs.  When she goes inside - say nothing, just clean it up and move on.  If you do this for awhile, #1 she'll go outside everytime you take her cause it's so much fun and #2 she'll learn how to ask to go outside cause it's so much fun!