Final answer:
Theodore Roosevelt's two major accomplishments were winning the Nobel Peace Prize for his mediation in the Russo-Japanese War and sending the Great White Fleet on a global tour to demonstrate American naval power.
Step-by-step explanation:
One of the two major accomplishments of Theodore Roosevelt was winning the Nobel Peace Prize for his mediation of the Russo-Japanese War, which helped end the conflict in 1905. This significant achievement showcased his dedication to international peace and diplomacy. Another major accomplishment during his presidency was sending the Great White Fleet on a goodwill tour around the world. This demonstration of American naval power sought to project American influence globally and was significant in establishing the United States as an emerging world power.
Roosevelt's reforms and policies significantly influenced the early 20th century and his presidency is remarked upon for its energy and vigour in tackling pressing issues of the time. Roosevelt's legacy as a progressive leader, military hero, and global peacemaker remains influential in American history.