In this question, specify and design a class called Location$3$D and implement it in a file Location$3$D$.$java. This class can be used to keep track of the position of a location in three$-$dimensional space. For example, point A in the below figure has three coordinates: $x=1\mathrm{.}0,y=0,$ and $z=1\mathrm{.}0.$

$(5$ pts$)$ The Location$3$D class contains the following instance variables:

Instance variables to store the three coordinates $x,y,z$ of a location.

An array of Location$3$D to store the $3$ nearest neighbors of the current location. For example, in the above figure, points $B,C,D$ are the $3$ nearest neighbors of $A.$

You are required to implement the following methods:

$(1)(5$ pts$)$ One no$-$argument constructor. This constructor sets null to all the variables with non$-$primitive data types and sets zero to double variables.

public Location$3$D$()$

$(2)(10$ pts$)$ One copy constructor that uses the given parameter obj to set the current object's instance variables. Need to be a deep copy. The precondition is that obj should not be null and should be an instance of Location$3$D$.$

public Location$3$D $($Object obj$)$

$(3)(10$ pts$)$ The clone method. Need to be deep copy.

$(4)(5$ pts$)$ The get and set methods of all the instance variables.

$(5)(10$ pts$)$ tostring $()$ method to generate a string representation of a location.

public String toString$()$

This method should organize the String information in the order of coordinates $x,y,z.$

$1$

$(6)(10$ pts$)$ equals method

This method returns true if the given object's $x,y,z$ are the same as $x,y,z$ of the given Location $3$D instance which activates this method. Otherwise, this method returns false. The precondition is that obj should not be null and should be an instance of the Location$3$D class.

public boolean equals $($Object obj$)$

$(7)(10$ pts$)$ A method to rotate the location by a specified angle around a specified axis.

public void rotate$($double theta, int axis$)$

To compute these rotations, you will need a bit of trigonometry. Suppose you have a location with coordinates $x,y,$ and $z.$ After rotating this location by angle $,$ the location will have new coordinates, which we will call $x^{\text{'}},y^{\text{'}},$ and $z^{\text{'}}.$ The equations for the new coordinates use the java.lang methods Math.sin and Math.cos$,$ as shown below:

After a $$ rotation around the $x-$asis $($i$.$e$.,$ axis $=0)$:

$x^{\text{'}}=x$

$y^{\text{'}}=ycos()-zsin()$

$z^{\text{'}}=ysin()+zcos()$

After a $$ rotation around the $y-$asis $($i$.$e$.,$ axis $=1)$:

$x^{\text{'}}=xcos()+zsin()$

$y^{\text{'}}=y$

After a $$ rotation around the $z-$asis $($i$.$e$.,$ axis $=2)$:

$x^{\text{'}}=xcos()-ysin()$

$y^{\text{'}}=xsin()+ycos()$

$z^{\text{'}}=z$

Question $2(30$ pts$)$

Write a class BankAccount to keep track of a balance in a bank account with a varying annual interest rate. The class has the following methods:

$(5$ pts$)$ The constructor will set both the balance and the annual interest rate to some initial values.

$(5$ pts$)$ The no$-$arguments constructor that sets both the balance and the interest rate to zero.

$(5$ pts$)$ The methods to change or retrieve the current balance or interest rate.

$(5$ pts$)$ The methods to make a deposit $($add to the balance$)$ or a withdrawal $($subtract from the balance$).$

$(5$ pts$)$ The method to add interest to the balance at the current interest rate. This method should have a parameter indicating how many years' worth of interest are to be added $($e$.$g$.,1$ year indicates that the account should have $1$ year's interest added$).$ You can use the following compound interest formula to calculate the interest:

Compound Interest $=$ Amount $-$ Principal

Amount $=P(1+\frac{r}{n}{)}^{nt}$

where,

$P=$ principal

$r=$ rate of interest

$2$

$n=$ number of times interest is compounded per year

$t=$ time $($in years$)$

Implement all the above methods. The correct declaration of class and instance variables gets $5$ pts$.$

Question $3(5$ pt

Write a main method to test the $2$ classes location$3$D and bankAccount.