(Algebra: quadratic equations) Design a class named QuadraticEquation for a quadratic equation $a x^2+b x+c-0$. The class contains:

• Private data fields $a, b$, and c that represent three coefficients.
• A constructor with the arguments for $a, b$, and $c$.
• Three getter methods for a, b, and c.
• A method named getDiscriminant () that returns the discriminant, which is $b^2-4 a c$.
• The methods named getRoot1 ( ) and getRoot2 () for returning two roots of the equation

$$r_1=\frac{-b+\sqrt{b^2-4 a c}}{2 a} \text { and } \quad r_2=\frac{-b-\sqrt{b^2-4 a c}}{2 a}$$

These methods are useful only if the discriminant is nonnegative. Let these methods return 0 if the discriminant is negative.

Draw the UML diagram for the class then implement the class. Write a test program that prompts the user to enter values for $a, b$, and $c$ and displays the result based on the discriminant. If the discriminant is positive, display the two roots. If the discriminant is 0 , display the one root. Otherwise, display "The equation has no roots." See Programming Exercise $3.1$ for sample runs.

The Account class) Design a class named Account that contains:

• A private int data field named $id$ for the account (default 0 ).
• A private double data field named balance for the account (default 0 ).
• A private double data field named annualinterestRate that stores the current interest rate (default 0 ). Assume that all accounts have the same interest rate.
• A private Date data field named datecreated that stores the date when the account was created.
• A no-arg constructor that creates a default account.
• A constructor that creates an account with the specified id and initial balance.
• The accessor and mutator methods for $\mathrm{id}$, balance, and annua InterestRate.
• The accessor method for dateCreated.
• A method named getMonth1yInterestRate () that returns the monthly interest rate.
• A method named getMonth1yInterest() that returns the monthly interest. A method named withdraw that withdraws a specified amount from the account.
• A method named deposit that deposits a specified amount to the account. Draw the UML diagram for the class then implement the class. (Hint: The method getMonthlyInterest () is to return monthly interest, not the interest rate. Monthly interest is balance * monthlyInterestRate. monthlyInterestRate is annualinterestRate / $12$. Note annualinterestRate is a percentage, for example $4.5 \%$. You need to divide it by $100$.)

Write a test program that creates an Account object with an account ID of $1122$ , a balance of $\$ 20,000$, and an annual interest rate of $4.5 \%$. Use the withdraw method to withdraw $\$ 2,500$, use the deposit method to deposit $\$ 3,000$, and print the balance, the monthly interest, and the date when this account was created.

What is the output of the following code ? public class A { boolean x; public static void main(String[] args) { A a = new A(); System.out.println(a.x); } }

When will a class have a default constructor?

(Stopwatch) Design a class named StopWatch. The class contains:

• Private data fields startTime and endTime with getter methods.
• A no-arg constructor that initializes startTime with the current time.
• A method named start () that resets the startTime to the current time.
• A method named stop () that sets the endTime to the current time.
• A method named getElapsedTime () that returns the elapsed time for the stopwatch in milliseconds.

Draw the UML diagram for the class then implement the class. Write a test program that measures the execution time of sorting $100,000$ numbers using selection sort.