The Nobel Peace Prize was first given out in 1901, so Abraham Lincoln is immediately disqualified, regardless of his wonderful accomplishments. The correct answer is that Woodrow Wilson was awarded the Nobel Peace Prize in 1919, for his work in founding the League of Nations in the years immediately after World War One.

Decolonization, in which the majority of European powers lost most of their foreign colonies, either willingly or unwillingly, took place in the years immediately after World War Two. Primarily this took place from 1946 to 1966. It was a time period that witnessed Britain and France in particular, but all the European powers, abandoning their massive imperial landholdings and returning to small nation-states. The primary motivating factors were the declining wealth and influence of European powers following the horrors of World War Two; the increased importance placed on individual and national rights in the second half of the twentieth century; and pressure from the United Nations and the United States.

The GI Bill was issued in 1944 as part of an extended program to help returning World War Two veterans reintegrate into American society. It provided, among other things, housing loans and grants for access to higher education. It is considered a very important factor in the creation of the massive American middle class.

The correct answer is "Isolationism." Put simply, the US was rather gun shy after the first world war. The unequaled level of destruction and loss of life of the first world war really put war into perspective, for both citizens and government, and led to a brief period of isolationism. In addition to the fact that WWI had just ended, the fact that the beginning of the second world war took place entirely in Europe (exactly like WWI) led isolationists to believe that intervention was the worst possible course of action. Thus, isolationists counseled avoidance of conflict at all cost. 

This is reflected in the preface of the "Neutrality Act" of 1935 (reproduced above). Note that the Act utterly and totally prohibits the export of arms to any belligerent, regardless of whether they were friend or foe.

"Atomic Bomb" is the correct answer. The United States became the first country to employ an atomic bomb in warfare, to great--if very controversial--success. The bombs dropped by the Enola Gay (the plane carrying both bombs) cause unprecedented destruction and eventually led to the surrender of the Japanese Empire, and the complete end of WWII.

The Cold War, which waged from the end of the Second World War until the fall of the Soviet Union, was primarily a conflict between capitalism and communism. It was essentially a conflict to see which economic system would become dominant in the world following the Second World War. The terms "democracy" and "socialism" are the two political systems that usually match with the economic systems of capitalism and communism, although it is possible to have a society that is both democratic and communist.

The first leader of Communist China was Mao Zedong. Mao was the founder of the Chinese Communist Party and the first ruler of the People’s Republic of China, which he governed from 1949 until 1976—when he died. Mao is notable for his role in the Chinese Civil War, leading the attack against the nationalists led by Chiang Kai-Shek. He is also notable for committing numerous atrocities, such as the Cultural Revolution, and for instituting the Great Leap Forward, designed to modernize the Chinese economy and solidify the hold of communism.

Mikhail Gorbachev, the last leader of the Soviet Union, ushered the country out of the Cold War and into an era of reforms and diminishing influence. His two major reforms are referred to as Glasnost and Perestroika. Glasnost was Gorbachev’s attempts to allow for greater political freedom; Perestroika was his attempt to restructure the soviet economy.

Joseph McCarthy was a United States senator in the late 1940s and early 1950s who famously led the crusade against prominent American communists. This period of American history is often referred to as The Red Scare, and the policy of attacking any known or suspected communists in Congress is called McCarthyism.

The Nationalist Party was led by Chiang Kai-Shek. During the Chinese Civil War the Nationalists faced off against the Communists, led by Mao Zedong. The Nationalists were eventually defeated and set up government in Taiwan.