The answer for that date is not available in the Jeopardy Archive (see related link) although the Archive does have a few shows for the tenth season they are mainly from the 1993 tournament of champions which ended on December 3 1993.
The Final Jeopardy category for July 12 2010 was Actors
The Final Jeopardy category for August 12 2010 was 19th Century Novrlists
The final Jeopardy category was New Sportsnew sportsNew Sports is the Jeopardy final category for April 12 2010New Sports is the Jeopardy final category for April 12 2010
The final category is Languages of Europe The clue was: A mixture of English and Spanish, LLanito is the language of this territory's 30,000 residents The answer was: What is Gibraltar
Jeopardy - 1984 1993 Celebrity Jeopardy Game 5 10-50 was released on: USA: 12 November 1993
Sunday
The final category was Documents
The final category is Shakespeare
Jeopardy - 1984 12-72 was released on: USA: 12 December 1995
Jeopardy - 1984 9-18 was released on: USA: 30 September 1992
Jeopardy - 1984 10-12 was released on: USA: 21 September 1993
Jeopardy - 1984 12-65 was released on: USA: 1 December 1995