Theresa May became Britain's second female prime minister yesterday.Once David Cameron had formally tendered his resignation to the queen at Buckingham Palace, chaired his final cabinet meeting and cracked jokes at Prime Minister's Questions for a last time, May was installed in No10 Downing Street in Whitehall - the official residence of the British leader.GOODBYES ALL ROUND: Outgoing UK Prime Minister David Cameron hugs his wife Samantha and their children on the doorstep of 10 Downing Street on his last day as British premier yesterday Picture: ANDY RAIN/EPAWhat's on the new boss's agenda?Meet the queen:May met Queen Elizabeth II at Buckingham Palace, where the monarch formally invited her to become prime minister.Make first speech as prime minister:From Buckingham Palace, she travelled with a police escort to Downing Street and spoke to the media before walking through the famous black door to be welcomed by her staff.HIGH TEA: David Cameron drives into Buckingham Palace to speak to the queen. Picture: DANIEL LEAL-OLIVAS/AFP PHOTOLetter of last resort:After being shown her new office and introduced to officials, one of May's first tasks will be to write the "letter of last resort".This letter tells commanders of the Trident missile submarine fleet how to respond in the event of a devastating nuclear attack against the UK.SHOO-IN: New UK Prime Minister Theresa May's penchant for fashionable footwear and dresses is widely referred to in British media Picture: EPAFirst, she will be briefed by Chief of the Defence Staff Sir Nicholas Houghton, who will explain the capabilities of a Trident missile.May will then be left alone to write four identical notes.The notes - which could include commands such as "retaliate" or "put yourself under the command of the US" - will be stored in two safes in the control room of each of the four submarines.SECONDS: A protester dressed as Theresa May holds up a placard outside No 10 Downing Street Picture: CARL COURT/GETTY IMAGESThey are destroyed after a prime minister leaves office so their content is known only to that leader.Hire the help:One of May's first tasks was to appoint a party chief whip, and then senior cabinet ministers. She promoted a string of women.Take calls from world leaders:US President Barack Obama, German Chancellor Angela Merkel and French President Francois Hollande called the new prime minister to offer congratulations.Tackle the in tray:Brexit;Immigration: she has promised to seek action on free movement but has admitted that leaving the EU will not immediately stem the flow of migrants from Europe;Social reform: May has promised a "radical programme of social reform" to help "ordinary working-class families";Renewing Trident: she must steer a parliamentary vote on the renewal of the Trident nuclear deterrent on Monday;High-speed rail 2: May is keen to push ahead with the controversial cross-country rail project, which she has said will boost the UK's economic growth;Heathrow: May said she would not take sides on the Heathrow Airport expansion project ahead of a formal cabinet decision;Tax evasion: a crackdown on individual and corporate tax avoidance and evasion is coming;Corporate responsibility: she plans to end the "fat cats" culture by giving shareholders the power to block excessive pay rises.Scotland: May wants Scotland consulted on Brexit but doesn't want it to leave the UK. - ©The Daily Telegraph..