Why did the United States declare war on the Empire of Japan on the 8th of December when Japan already gave them a declaration of war? Was it to show public support or to try to recover some morale?
I can't be certain without more information, but based on your question, it seems like you mistakenly believe that the Japanese diplomats in Washington D.C. delivered a declaration of war to the United States on December 7. They did not, but this is a common misconception. U/lubyak's answer and my answer in this thread can provide more information on the message the Japanese diplomats did deliver.
In addition, I answered in this thread why the United States waited to declare war until December 8. Basically, the attack occured much later in the day in Washington than in Hawaii (where it was morning), and President Roosevelt had to assemble Congress to ask for a vote.
I think those two threads should answer your question but if I've misunderstood you, please let me know.