An employee doing quality control at a screw factory uses the following measurements to check the diameter of the screws. (1 mark) \[ 7.85 \mathrm{~mm}_{-0.06 \mathrm{~mm}}^{+0.12 \mathrm{~mm}} \] State the tolerance of the measurement.

Find the topology generated in \( R \) by the class of all closed sub-intervals of the type \( [a, a+11 \). ( 4 Marks)

Esercizio 17.2 Sia \( F \) l'endomorfismo di \( \mathbb{R}^{3} \) associato alla matrice \( A=\left(\begin{array}{ccc}1 & -3 & 1 \\ -3 & -2 & 0 \\ 1 & 0 & -2\end{array}\right) \) rispetto alla base canonica. (4) Scrivere l'espressione generale di \( F \). (i) Usando la definizione data, verificare che \( F \) è un endomorfismo simmetrico. (iii) Diagonalizzare \( F \) rispetto ad una base ortonormale di \( \mathbb{R}^{2} \) di autovettori per \( F \).

One aspect of digital transformation is adopting Artificial Intelligence (AI) in business processes. However, AI is not without problems. Discuss ANY THREE (3) organisational risks as well as ANY TWO (2) customer risks associated with AI.

Problema A.1. Dadas las matrices cuadradas \[ I=\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right) \quad \text { y } \quad A=\left(\begin{array}{rrr}2 & 1 & 1 \\ 2 & 3 & 2 \\ -3 & -3 & -2\end{array}\right) \text {, } \] se pide: a) Calcular las matrices \( (A-I)^{2} \) y \( A(A-2 I) \). (4 puntos). b) Justificar razonadamente que b.1) Existen las matrices inversas de las matrices \( A \) y \( A-2 I .(2 \) puntos). b.2) No existe matriz inversa de la matriz \( A-I \). (2 puntos). c) Determinar el valor del parámetro real \( \lambda \) para el que se verifica \( A^{-1}=\lambda(A-2 I) \quad(2 \) punt

Topological space. Let \( X=\{a, b, c, d, e\} \) and \( T=\{\phi, X,(a),\{b\},\{a, b\},(c),(a, b, c),\{a, c),\{b, c)\} \), Let \( E=(a, b \) (s). Find the closure and interior of \( E \)