Notes, summaries, assignments, exams, and problems for Baccalaureate

Question 6: Vector Spaces and Subspaces

Finding the Zero Vector

1. Take the general scalar multiplication formula r ◦ (a, b, c, d).
2. Plug in r = 0.
3. Read off the resulting matrix; that is the zero vector. (Note: 0 ◦ anything = the zero vector in any vector space.)

Proving a Subset U is a Subspace

1. Identify which entries of U are locked (fixed numbers) and which are free (variables).
2. Check if the zero vector (from part a) fits the locked entries of U.
3. Take two general elements of U (using the same locked numbers but different free letters) and combine them with addition. Check that the locked entries stay locked.
4. Take one general element of U and scale it with ◦. Check that the locked entries stay locked.
5. If all three subspace conditions hold, then U

Art and Society: Analysis and Exercises

Part A: Maya Dahir and Art History

• A3. Maya Dahir’s Artwork: TRUE – "Despite initial criticism, her work later gained recognition."
• A4. The Purpose of Embracing Our: FALSE – "Held an exhibition in the US in 2022 to encourage young artists to explore global issues."
• A5. Art’s Influence On: FALSE – "From ancient pyramids to Internet memes, art has always influenced society and culture."
• A6. Picasso’s Painting Inspiration: FALSE – "Bringing the stories of civilian experiences from the war to the world’s attention."

Vocabulary Definitions

• A7.1: "Very old" – Ancient
• A7.2: "Appreciation" – Recognition
• A8.1: "Very difficult experiences" – Struggles
• A8.2: "People who give…" – Supporters

Part B:

## Amino Acids and Peptides
### 1. \alpha-Amino Acids: Structure and Classification
Amino acids are the fundamental building blocks of proteins. An **\alpha-amino acid** consists of a central \alpha-carbon atom bonded to four distinct groups: an amino group (-\text{NH}_2), a carboxylic acid group (-\text{COOH}), a hydrogen atom (-\text{H}), and a variable side chain (-\text{R}).
#### Classification based on R-group polarity:
 * **Non-polar / Hydrophobic:** Side chains are aliphatic hydrocarbons or aromatic rings (e.G., Alanine, Valine, Phenylalanine).
 * **Polar / Uncharged:** Side chains contain hydrophilic groups like hydroxyls or amides (e.G., Serine, Glutamine).
 * **Acidic / Negatively Charged:** Side chains contain an extra carboxyl group... Continue reading "Bioelements and their importance" »

1. Single-Cell Protein & Alcohol Production

Industrial fermentation harnesses microbial metabolism under controlled conditions to synthesize biomass and primary metabolites on a massive commercial scale.

                  [Raw Material / Carbon Source]
                                 │
                                 ▼
         ┌──────────────────────┴──────────────────────┐
         ▼                                             ▼
 [Biomass Production]                       [Metabolite Production]
  e.g., Single-Cell Protein                  e.g., Ethanol Fermentation
  (Cell body is the product)                 (Secreted fluid is the product)

Lecture 1: Introduction and Security Concepts

The CIA Triad

• Confidentiality: Limits access to authorized users. A breach results in unauthorized disclosure.
• Integrity: Prevents unauthorized modification. A breach results in an altered document.
• Availability: Ensures timely access. A breach results in a Denial of Service (DoS) attack.

Additional Security Objectives

• Authenticity: Verifies that the data or sender is real and trustworthy.
• Accountability: Ensures actions are traceable to specific entities.
• Non-repudiation: Ensures a party cannot deny their actions, often achieved via digital signatures.

Kerckhoffs's Principle

Security should rely only on the secrecy of the key, not the secrecy of the algorithm. The system remains secure even if the attacker... Continue reading "Modern Cryptography and Data Security Fundamentals" »

Essential Film and Cinema Vocabulary

• Come out: Estrenarse
• Compose: Componer
• Cut off: Interrumpir
• Dragged: Se alargó demasiado
• Relate to: Identificarse con
• Starred in: Protagonizó
• Turn up: Subir (volumen)
• Appeals to: Atrae a
• Audience: Público
• Broadcast: Emitir
• Catchy: Pegadizo
• Letdown: Decepción
• Live performance: Actuación en vivo
• Long-running: De larga duración
• Outstanding: Excepcional
• Overrated: Sobrevalorado
• Recording: Grabación
• Remake: Nueva versión
• Stunning: Impresionante
• Venue: Lugar
• Worth seeing: Que vale la pena ver

Going to the Cinema: Pros and Cons

Many people enjoy going to the cinema, while others prefer watching films at home. There are both advantages and disadvantages to this experience.

The Advantages

On the one hand, going to the cinema can... Continue reading "Cinema vs Home Viewing: Pros, Cons and Film Review Tips" »

Part 1: Word-Formation Examples

1. Reversative verb: uncork — to reverse the state of being corked/sealed.
2. Locative noun: bakery — a noun denoting a place where something happens or has a specific function; here, a place where baking occurs.
3. Denominal verb: cannibalize — a verb derived from a noun (cannibal).
4. Diminutive noun: duckling — a noun with the diminutive suffix -ling, indicating a small or young duck.
5. Attenuative adjective: None from the set. An attenuative adjective expresses a lessened degree of a quality (e.g., greenish). Indecisive is negative/privative, not attenuative.
6. Repetitive verb: replay — a verb with the prefix re-, indicating an action done again.
7. Collective noun: aristocracy — a noun referring to a collective social

1) DIJKSTRA (SSSP) — STEP TABLE (PAST-PAPER INSTANCE A)

Given edges: a→b(2), a→c(7), a→e(10), b→d(2), c→d(1), c→g(2), d→f(2), e→g(1), f→g(2). Source = a.
Rule: Pick unsettled vertex with minimum dist; relax outgoing edges.

Vertices:   a   b   c   d   e   f   g

Init:
Dist      = 0   2   7   ∞  10   ∞   ∞
S = ∅

Step 1: Pick a (min=0), S={a}
Relax from a: already set b=2, c=7, e=10
Dist      = 0   2   7   ∞  10   ∞   ∞

Step 2: Pick b (min=2), S={a,b}
Relax b→d: dist(d) = dist(b)+2 = 2+2 = 4
Dist      = 0   2   7   4  10   ∞   ∞

Step 3: Pick d (min=4), S={a,b,d}
Relax d→f: dist(f) = 4+2 = 6
Dist      = 0   2   7   4  10   6   ∞

Step 4: Pick f (min=6), S={a,b,d,f}
Relax f→g: dist(g) = 6+2 = 8
Dist

Meaning and Definitions of Sociology

Etymological: From Latin socius (companion/society) and Greek logos (study/science) – literally, the "science of society".

Scientific Study: It is a systematic, empirical study of human society, social behavior, patterns, and relationships, using scientific methods to understand social phenomena, unlike mere philosophical speculation.

Key Focus Areas: Social structure, social institutions (family, education, religion), social interaction, culture, and the impact of society on individual behavior.

Definitions of Sociology

• Auguste Comte (Father of Sociology): Defined sociology as the science of social phenomena, aiming to discover the laws governing society.
• M. Ginsberg: "Sociology is the study of human interactions

Template for Pros and Cons Essays

Follow these guidelines strictly to structure your argument effectively.

Introduction

[1. IDEA GENERAL] have become central to modern life. [2. IDEA ESPECÍFICA SOBRE EL TEMA]. For this reason, the advantages and disadvantages of [TEMA] have become a matter that deserves our attention.

The Advantages

On the one hand, [TEMA] is praised for its capacity to [VENTAJA PRINCIPAL]. This often results in [UN BENEFICIO CONCRETO Y TANGIBLE]. Moreover, it can [OTRA VENTAJA IMPORTANTE, preferiblemente de tipo social o personal].

The Disadvantages

On the other hand, [TEMA] is also criticised for its tendency to [DESVENTAJA PRINCIPAL]. A clear example is how it [MENCIONAR UN ASPECTO O MECANISMO CONCRETO], which frequently leads... Continue reading "Pros and Cons: A Balanced Analysis Framework" »