Note: Please write your solutions on the answer sheet.

$1.$ An online vehicle renting software is used to process online vehicle renting business. Customers can rent different types of vehicles such as cars, buses, vans and trucks. Cars and buses are used for passenger transportation with different capacity. Vans and trucks are used for freight transport with different load capacities. Vehicles rented on this software are not owned by the software provider, but owned by different third$-$party persons or companies. Customers need to sign a contract for renting a vehicle about the price and period of the renting with the owner of the vehicle. Other software can communicate with this vehicle booking software to support the booking of vehicles from third$-$party software too.

$(1)$ Prepare a domain class diagram for this software including classes "vehicle, car, bus, truck, van, customer, owner, contrast, etc" $(10\text{'})$

$(2)$ Build an application class diagram for the system by adding boundary, user interface and controller classes. $(10\text{'})$

$2.$ When a mobile phone is in the sleeping state, its screen is turned off. When the power button is short$-$pressed, it changes to the password entering state. If the correct password is input, the mobile phone is awoke and you can use Apps in the phone. If the password is not correctly input for five times, the mobile phone will be locked temporarily for $30$ minutes. After $30$ minutes, it changes to the normal sleeping state, user can awake it again by entering correct password. In the entering password and awaken state, it will change to sleeping state if no operations are input. If the power button is long$-$pressed for $5$ seconds, it changes to the powered off state no matter what the current state is$.$ When the mobile phone is powered off, it changes to the entering password state when the power button is long pressed for $5$ seconds.

$(1)$ Build a state diagram for the mobile phone. $(15\text{'})$