**Exercise 07.1 **Write a method `static double scalarProduct(double[] A,
double[] B)` that calculates the scalar product of two arrays `A` and
`B`, assuming they have the same length. We recall that the
*scalar product* of `A` and `B` is obtained as the sum of
the products `A[i]*B[i]`, for all `i`, with 0 < = *i* <
`A.length`.

**Exercise 07.2 **Write a method `static int[] intersection(int[] A, int[]
B)` that returns a new array containing the intersection of two arrays
`A` and `B`, i.e., exactly those elements that are present both
in `A` and in `B` (independently of their position). We may
assume that `A` and `B` do not contain duplicates, i.e., elements
that appear more than once in the array.

**Exercise 07.3 **Write a method `static double[][] transposeMatrix(double[][]
M)` that returns a new matrix that is the transpose of the matrix
`M`. We recall that the *transpose* of a matrix `M` is
obtained by exchanging the rows with the columns, which corresponds to exchange
`M[i][j]` with `M[j][i]`, for each pair of valid indexes
`i` and `j`.

**Exercise 07.4 **Write a method, `static int[] matrixSumColumns(int[][])`,
that takes as parameter a matrix and returns an array with one element for each
column of the matrix; the element of index `i` of the array must be
equal to the sum of the elements of column `i` of the matrix.

**Exercise 07.5 **Write a predicate `static boolean equalArrays(int[] A, int[]
B)` that returns `true` if the two arrays `A` and `B`
are equal (i.e., `A[i]` is equal to `B[i]`, for each `i`),
and `false` otherwise.

**Exercise 07.6 **A *duplicate* in an array is a value that appears more than
once as element of the array. Write a method `static int
numberOfDuplicates(int[] A)` that returns the number of distinct duplicates in
the array `A`. Write also a method `static int
numberOfDistinctValues(int[] A)` that returns the number of distinct values in
the array `A`.

**Exercise 07.7 **Write a method `static int[] removeDuplicates(int[] A)` that
returns a new array obtained from `A` by removing all duplicates. The
duplicates should be removed by keeping only the first occurrence of each
distinct element, and shifting remaining elements upwards when a duplicate is
removed.

**Exercise 07.8 **What does the following method calculate?

public static int mystery(int[] A) { int x = 0; for (int i = 0; i < A.length; i++) if (A[i] % 2 == 1) x++; return x; }

**Exercise 07.9 **A matrix `M` is said to be *symmetric* if it is square
(i.e., has the same number of rows and columns) and `M[i][j]` is equal
to `M[j][i]`, for each pair of valid indexes `i` and `j`.
Write a predicate `static boolean symmetric(int[][] M)` that returns
`true` if the matrix `M` is symmetric, and `false`
otherwise.

**Exercise 07.10 **A matrix `M` is said to be *lower triangular* if all
elements `M[i][j]` with `i<j` (i.e., that are "above" the main
diagonal) are equal to 0. Write a predicate `static boolean
lowerTriangular(int[][] M)` that returns `true` if the matrix
`M` is lower triangular, and `false` otherwise.

**Exercise 07.11 **A matrix `M` is said to be *diagonal* if all elements
`M[i][j]` with `i` different from `j` (i.e., that are not
on the main diagonal) are equal to 0. Write a predicate `static boolean
diagonal(int[][] M)` that returns `true` if the matrix `M` is
diagonal, and `false` otherwise.

**Exercise 07.12 **Realize a Java class `Apartment`, whose objects maintain the
following information: an integer that indicates the size in square meters of
the apartment, the address, and a list of maximal 10 names of persons that
live in the apartment. Each person living in the apartment has an associated
number between 0 and the number of persons currently living in the apartment
minus 1. The class should export the following functionalities:

- a constructor that takes a size and an address and creates an apartment that is initially empty;
- a method that returns the size of the apartment;
- a method that returns the address of the apartment;
- a method that returns the number of persons currently living in the apartment;
- a method that takes as parameter the name of a person, and adds the person to those living in the apartment; the person gets assigned the next available number, if there is still room; if the apartment is full (i.e., 10 persons already live there), the method does nothing;
- a method that takes as parameter a nonnegative integer number and returns the name of the person associated to that number and living in the apartment; if the number is greater than or equal to the number of persons in the apartment, the method returns null;
- a method that takes as parameter a nonnegative integer number and removes the person associated to that number from the apartment; the number associated to all following persons should be decreased by one; if the number is greater than or equal to the number of persons in the apartment, the method does nothing.
- a method
`toString`that does overriding of`toString`inherited from object, and returns a string with all the information about the apartment.