Final answer:
Eisenhower's establishment of NASA in 1958 and his support for the National Defense Education Act demonstrate his awareness of the Cold War tensions with the Soviet Union, particularly in technological and scientific fields, such as the space race.
Step-by-step explanation:
The clear indicators that President Dwight D. Eisenhower was aware of the mounting tensions between the United States and the Soviet Union during the Cold War can be found in various actions he took during his presidency. One significant action was his establishment of the National Aeronautics and Space Administration (NASA) in 1958, prompted by the Soviet Union's advancements in space with the successful launch of Sputnik. Eisenhower signed NASA into existence as a civilian agency focused on peaceful space exploration, emphasizing the scientific purposes over military uses, which reflects his understanding of the international implications of the space race. By advocating for space exploration in a non-military framework, he also aimed to avoid the escalation of tensions while ensuring the U.S. did not fall behind in technological advancement.
In response to evidence such as the launch of the Soviet satellite, Eisenhower prioritized the consolidation of aeronautical research into NASA and supported the National Defense Education Act to facilitate improvements in science and technology education, further showing his consciousness of the U.S.-Soviet rivalry. He was careful to counsel that space achievements by the Soviets set an important precedent that could be advantageous for U.S. strategies. This indicates that Eisenhower recognized the potential for space to become a new domain for both nations to assert their technological prowess without the immediate risk of military confrontation.