The sentences that do not use brackets correctly are:
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In 1911 Marya Sklodowska [also known as Madame Curiel won the Nobel Prize in chemistry. (The opening bracket has no matching closing bracket; it should be closed before "won".)
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Known as the "Father of Tragedy," Aeschylus [525-456 BCE) was a prominent Greek playwright. (The brackets are mismatched; the opening bracket is "[", and the closing bracket is ")", which is incorrect.)
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Dr. Janusch began his experiments during the 1920s [See pages 33 and 34), but the turning point in his work came in 1935. (This also has mismatched brackets; the opening bracket is "[", and the closing bracket is ")", which is incorrect.)
The fourth sentence, "The feature of the day is the Hubble Telescope movie of Neptune (found on the website of the National Aeronautics and Space Administration [NASA])." uses the brackets correctly.