It is the age! My daughter went through the same thing and still at 20 does some things half way. To them, when you ask them to do something and then show them how to do it, it is saying that I want you to do this, but it has to be my way or it is wrong.
Pick your battles. If you don't feel that the way she vacumns is "RIGHT" and you can't live with the way she does it, then pick something else for her to do. I always made my daughter do it anyway, and would tell her that if she was going to spend 3 minutes doing her chores, then she could only have 3 minutes on the phone, tv, video games, etc.
If she does not think it is worth "earning money" for, then don't give her any when she wants to do something. Buy only her necessities and no extras, she will eventually figure out that "chores" really do pay.
As far as her room goes, if she doesn't want to clean it and keep it reasonable (remember she is 11 and they are still learning their organizational skills) then just shut the door and tell her that her room has to be cleaned by a certain day of the week and if not, you will clean it for her and keep everything you pick up that is not in a where it should be. (Remember, if you tell her the book is suppose to be on the desk and it is there but is crooked or not exactly where you would put it, she still has it where it is suppose to be.)
I would do this, and for everything I picked up, I would put in a plastic bag and either put in the garage or I sold at a yard sale (and no I didn't replace it down the road). The clothes I would wash and dry and keep. I eventually ended up with all my daughters clothing and when she wanted something she had to bring me what she had had own and then I would give her another set of clothes to wear (of which, I picked out the outfit). Eventually she figured that out, and decided that it was easier to take care of her own clothes and wear what she wanted than my way.
The hygiene part will find its way. Remember she is in that stage from going from you taking care of her to her finding her own way and learning to be a young lady. Her friends will let her know about her hygiene. Just reassure her that you don't want anyone making fun of her because of it and you will let her do it her way, but you are always there to help if she would like it. Make sure she has all the products that she needs to do the job (there are even a couple of dvd games for computers where they can try different styles of hair, clothes, makeup etc.) and then when see she has made an effort (no matter how small) Praise her, Praise her, and Praise her some more and only Praise her. Dont's say "wow, you did a great job on this, but you could have done better on that"!
Pick the battles worth fighting and the others leave on the battlefield, she will figure it out.
Hope this helps,
Thin hair and gray mother of 20 year old daughter and 4 boys.