US Commodore Mathew Perry came in this country in 1853. He ordered its emperor among other things, to accept the very reasonable requests from US. This country was

Japan.

The country that Commodore Matthew Perry came to in 1853 and made demands of its emperor was Japan.

The country that Commodore Matthew Perry visited in 1853 and presented the emperor with a list of demands was Japan. Japan at that time was ruled by the Tokugawa Shogunate, and it had a policy of isolation from the rest of the world, known as the sakoku policy. Perry's visit, known as the Perry Expedition, was an attempt by the United States to establish trade relations with Japan and gain access to its ports.

To find the answer to this question, you could have taken the following steps:

1. Recall or research the historical events related to Commodore Matthew Perry in the mid-19th century.
2. Remember or look up the details of the countries involved in the Perry Expedition.
3. Identify the country where Perry visited and presented demands to its emperor, which was Japan.