Notes, summaries, assignments, exams, and problems

1. Simplifying Algebraic Expressions

How to Simplify Algebraic Expressions

• Multiply numbers and letters together.
• Combine like terms (terms with the same letters and powers).

Example:
−2ac × 4bd = −8abcd

Example:
5ab − 8b²a + ba = 5ab − 8ab² + ab = −8ab² + 6ab

2. Expanding Brackets (Distributive Law)

How to Expand Brackets

• Multiply everything inside the bracket by what is outside.

Example:
−4(x + 7) = −4x − 28

Example:
5(x − 3) + 2(6 − x) = 5x − 15 + 12 − 2x = 3x − 3

3. Solving Equations

How to Solve Equations

• Get all variables (e.g., x's) on one side and numbers on the other.
• Perform the same operation on both sides of the equation.

Example:
3x + 2 = 17
3x = 15
x = 5

Example:
9x − 8 = 4x + 7
5x = 15
x = 3

4. Solving Inequalities

How

Maritime Meteorological Glossary

General Terms

Backing

Rolando

Becoming

Volverse

Blizzard

Ventisca

Cloud

Nube

Cloudy

Nuboso

Cold front

Frente frío

Current (jet stream)

Corriente de chorro

Cyclone

Ciclón

Dangerous semicircle

Semicírculo peligroso

Decreasing

Disminuyendo

Deepening

Profundizándose

Dense fog

Densa niebla

Dew point

Punto de rocío

Drizzle

Llovizna

Eastern

Oriental

Western

Occidental

Expected

Esperada

Eye of the storm

Ojo de la tempestad

Fair

Bueno

Filling

Rellenándose

Flow

Flujo

Fog patches

Bancos de niebla

Fog

Niebla

For a time

Por algún tiempo

Force

Fuerza

Forecast

Predicción

Front

Frente

Frost

Helada

Gale warning

Aviso de temporal

General synopsis

Situación general

GMT / UTC

Hora Greenwich / Hora universal

Gusts

Rachas

Heavy rain

Lluvia fuerte

High

Alta presión

High clouds

Nubes altas

Horse

Key Indigenous Concepts and Terminology

• Indigenous Historical Consciousness: The understanding of relationships between past, present, and future from an Indigenous perspective.
• Historicity: The idea that history is actively made and revolves around Indigenous peoples.
• Historical Recognition: Acknowledging the full and accurate historical narratives of Indigenous peoples.
• Sites of Pedagogy: Specific locations or contexts that serve as places of learning.
• Indigenousness: The holistic way of being, encompassing the deep connection between land and people as a whole.
• Sovereignty: The inherent right to self-governance and full rights for Indigenous nations.
• Métissage: The interweaving or separation of histories, often referring to cultural mixing or

Core Concepts in Compiler Design

Compiler

Compiler: Translates entire source code to target code before execution. It requires a full parse and upfront error checking, then executes the generated target code.

Interpreter

Interpreter: Executes source code incrementally (line-by-line or statement-by-statement). It translates and executes on the fly, and may partially execute ill-formed programs until an error is encountered.

LVar vs. x86 Architecture

LVar: Features nested expressions, implicit control flow (represented by an Abstract Syntax Tree - AST), and an unlimited number of logical variables.

x86: Characterized by flat instructions, atomic operands (registers/memory), explicit control flow (jumps), and a limited set of registers. Compilation passes... Continue reading "Core Concepts in Compiler Design and Language Runtime" »

English Vocabulary: Social Action and Community Engagement

Unit 4: Social Action Vocabulary

• Attend a rally: asistir a una manifestación
• Appeal: recurrir
• Campaign
• Campaigner
• Charity
• Donate / Donation
• Fundraising event: evento para recaudar fondos
• Fundraiser: recaudador de fondos
• Go on a march: ir a una marcha
• Raise awareness of: concienciar / sensibilizar
• Raise funds / money: recaudar fondos
• Sign a petition: firmar una petición
• Sit-in: sentada
• Sponsor: patrocinar
• Sponsorship: patrocinio / apadrinamiento
• Take part in a [cause/event]
• Volunteer
• Voluntary work

Unit 4: Key Collocations

• Animal charity
• Beach clean-up
• Cancer research
• Computer game
• Death penalty
• Endangered species
• Free debate
• Homeless person
• Informed decision
• Political engagement: compromiso político
• Legal age:

BPSK Signal Generation

This section demonstrates the generation of a Binary Phase Shift Keying (BPSK) signal using Python.

import numpy as np
import matplotlib.pyplot as plt

def bpsk_detect(modulated_signal, carrier):
    return np.sign(modulated_signal * carrier)

message_frequency = 10
carrier_frequency = 20
sampling_frequency = 30 * carrier_frequency
t = np.arange(0, 4/carrier_frequency, 1/sampling_frequency)
message = np.sign(np.cos(2 * np.pi * message_frequency * t) + np.random.normal(scale = 0.01, size = len(t)))
carrier = np.cos(2 * np.pi * sampling_frequency/carrier_frequency * t)
modulated_signal = carrier * message
detected_message = bpsk_detect(modulated_signal, carrier)

plt.figure(figsize=(12, 8))
plt.subplot(4, 1, 1)
plt.plot(t,

Understanding Hybristophilia: Attraction to Criminals

Key Terminology Related to Hybristophilia

• Heinous: Horrible, extremely evil (atroz).
• Assault: A violent physical attack (agresión).
• Paraphilia: A condition characterized by abnormal sexual desire or activities (parafilia).
• Notoriety: The state of being famous or well-known, especially for something bad (mala fama).
• Hostage: A prisoner taken (rehén).
• Oppressor: One who treats people cruelly.
• Reciprocity: A mutual exchange of benefits, help, and support in a relationship.
• Susceptible: Easily influenced.
• Obscure: Not clear.
• Deed: An act (acción o hecho).
• Captor: One who takes a hostage.
• Allure: Attraction, charm (atraer).

Defining Hybristophilia

The term Hybristophilia is derived from the Greek roots:... Continue reading "Defining Hybristophilia, Sharenting, and Health Concepts" »

Church of La Vera Cruz, Segovia (12th Century)

• Centralized scheme floorplan
• Based on Dome of the Rock & Holy Sepulchre
• Central edicule
• Three apses head
• Quadrilateral bell tower
• Twelve-sided plan
• Two floors
• Buttresses
• Ribbed vault & Caliphal dome

Holy Sepulchre, Torres del Rio, Navarra (12th Century)

• C Templarios
• Octagonal plan
• Tower to get to the lantern
• Mudejar precedents
• Arabic star-shaped dome
• Apse in East
• Archivolts
• Parallel ribs
• Stone dome
• Pointed/midpoint arches

Templarios de Eunate Church, Navarra (12th Century)

• External cloister enclosing the Church
• East apse
• Tower with spiral stairs
• Ribs in dome pass through center
• Octagonal plan
• Dome starts in columns
• Midpoint arch

Cathedrals of St. James (11th Century)

• Central nave with barrel vaults
• Arches and transversal

Visigothic Architecture (7th Century)

• Key characteristics: Austerity, simplicity, portico, nave, transept, north/south portico, presbytery, apse.

San Pedro de la Nave, Zamora

• Greek or Latin cross plan within a rectangle
• Influenced by Greek and Roman precedents
• Small scale and spaces
• Reflects a simpler technique, indicative of a decline in craftsmanship
• Reassembled in a different location
• Naive or stylized sculptures
• Thick walls
• Lantern at the geometrical center

San Juan de Baños, Palencia

• Three naves
• Commissioned by King Recesvinto
• Monolithic interior columns
• Appendix (or side chapels)
• Pointed horseshoe arches
• Constructed with yellow sandstone ashlar
• Trident floor plan

Quintanilla de las Viñas, Burgos

• Latin cross plan
• Three naves
• One transept
• Features vegetal motifs
• Animal

Conditionals

Zero Conditional

If + present simple, ... present simple

First Conditional

If + present simple, ... will + infinitive

Second Conditional

If + past simple, ... would + infinitive

Third Conditional

If + past perfect, ... would + have + past participle

The Passive Voice (Active/Passive)

Present Simple

Active: The waiter serves the customers.

Passive: The customers are served by the waiter.

Present Continuous

Active: The waiter is serving the customers.

Passive: The customers are being served by the waiter.

Past Simple

Active: The waiter served the customers.

Passive: The customers were served by the waiter.

Past Continuous

Active: The waiter was serving the customers.

Passive: The customers were being served by the waiter.

Present Perfect Simple

Active:... Continue reading "English Grammar and Vocabulary Guide: Conditionals, Passive Voice, and More" »