Rex Albert Cooper was born in Randwick New South Wales on the 10 June 1920 to John Joseph Thomas and Harriet Ethel Cooper. He enlisted in the Royal Australian Navy on the 10 June 1938 for a period of 12 years. He was assigned to HMAS Cerberus for initial training before being assigned to HMAS Sydney (II) on the 29 September 1938.
During 1940 Copper, on board HMAS Sydney, saw service in the Mediterranean where she had survived intense air attacks and sank the Italian cruiser Bartolomeo Colleoni. When Cooper and the HMAS Sydney returned home to Sydney in February 1941, he along with the rest of the crew received a hero's welcome. For the next nine months, the work on board the Sydney was routine as it carried out patrol and escort duties in the Pacific and Indian oceans.
On 19 November 1941 during a return voyage to Fremantle that she encountered the HSK Kormoran. Disguised as a Dutch merchant vessel, the Komoran used the advantage of surprise and brought all its armament to bear on Sydney II. By now the two ships were less than 2 kilometres apart. In the bitter battle that followed both ships were badly damaged and the German sailors were forced to abandon ship. They watched the Sydney disappear into the night until it became a distant glow on the horizon.
At some point during the night of the 20 November 1941, Sydney II lost buoyancy and sank losing all 645 men on board.
Rex Albert Copper is commemorated on the Plymouth Naval Memorial, Plymouth England.