1. The Eisenhower presidency, despite two recessions, was for the most part a period of continuing economic prosperity in the United States.

----------------------my answer: true
Because during president Eisenhow's presidency, the economy grew rapidly and brought prospeity to many americans.

2.The demands of black Americans subsided significantly during the 1960s.
----------------------my answer: True
my book didn't specify about the demand of black american in 1960s. it only talk about then when automation greatly increased the productivity. But since the 1960s were about black americans wanted equal rights and separating the black americans with the white americans, i guess it will true.

it is correct?

I think you need to re-think both answers.

http://historicaltextarchive.com/sections.php?op=viewarticle&artid=537

http://www.google.com/search?q=blacks+and+1960s&rls=com.microsoft:en-us:IE-SearchBox&ie=UTF-8&oe=UTF-8&sourceid=ie7&rlz=1I7SUNA

The civil rights movement didn't end with the 1960s.