I want to get a Cooler Master SGC-1000-KWN1 Storm Enforcer ATX mid Tower Computer case will a Diamond 7970PE53G Radeon HD 7970 Video Card Fit in the case useing a N-Alvorix-RS880-uATX as the Motherboard
Yes, it will. And from looking up your motherboard it appears to be a board make for HP and it's a uATX so I'm not sure if that board will fit in the Cooler Master unless uATX is the same as micro ATX. And just out of curiosity, are you wanting to use the PSU from the HP?
Yes uATX is the same as mATX; they have the same dimensions: 24.4x24.4cm / 9.6x9.6".
And it looks to me like the mounting holes are in the same location as standard mATX, so it will fit in the Storm Enforcer.
According to Diamond's website the 7970PE53G is 11.6" long (29.5cm).
According to CM's website the Storm Enforcer can fit graphics cards up to 27cm with the harddrive bay installed and 39cm with it removed. So you will have to remove the middle HDD cage to fit the 7970 in, but this is a simple procedure.