Fluid Statics (Fluids at Rest)〰️

a) Density (ρ)

Defined as mass per unit volume
ρ = m / V
Unit: kg/m³


b) Pressure in Fluids

Pressure is the force applied per unit area:
P = F / A
Unit: Pascal (Pa)


c) Pressure due to a Column of Fluid

P = ρgh
Where:

ρ = density of the fluid

g = gravitational acceleration

h = height/depth of the fluid



d) Pascal’s Principle

A change in pressure applied to an enclosed fluid is transmitted equally throughout the fluid.
Used in hydraulic systems.


e) Archimedes’ Principle

A body submerged in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid.
F_b = ρ_fluid × g × V_displaced


f) Conditions of Floating and Sinking

✅Floating: Weight = Buoyant force

✅Sinking: Weight > Buoyant force

✅Suspended: Weight = Buoyant force (object remains at equilibrium)

Heart Chambers

✅The human heart has four chambers

1. Right Atrium – receives deoxygenated blood from the body via the vena cava.


2. Right Ventricle – pumps deoxygenated blood to the lungs through the pulmonary artery.


3. Left Atrium – receives oxygenated blood from the lungs via the pulmonary veins.


4. Left Ventricle – pumps oxygenated blood to the body through the aorta.



💡 The atria (plural of atrium) are the upper chambers and have thin walls, while the ventricles are the lower chambers and have thick, muscular walls—especially the left ventricle, which pumps blood to the whole body.

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❓What is the correct sequence of blood flow through the heart chambers, starting from the body?(USSLCE 2016)

A. Right atrium → Right ventricle → Lungs → Left atrium → Left ventricle → Body

B. Left atrium → Left ventricle → Lungs → Right atrium → Right ventricle → Body

C. Right ventricle → Right atrium → Lungs → Left ventricle → Left atrium → Body

D. Right atrium → Left atrium → Right ventricle → Left ventricle → Body

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traning date of online exam, model and final exam date (entrance)

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❓What is the simplified form of a-¹b-¹/a-³_ b-³ ? (UEE 2011)

A. a²b²/b²_ a²

B. a³_ b³/ab

C. a²b²/b³_ a³

D. a³_ b³/a_b

Paper or online is better for memory 🤔

🛡 Paper-Based: Better for Memory

Writing by hand improves memory – Studies show handwriting helps your brain process and remember information more deeply.

You can annotate – Underline, circle, or make notes on the question paper, which helps focus.

More time to think – No rush from clicking fast; you engage more slowly and deeply.


⚠️ Online: Sometimes Less Effective for Memory

Typing doesn't strengthen memory as much as writing by hand.

Distractions are easier – It’s tempting to rush or click randomly.

Less interaction with content – You can’t mark the screen easily like you can on paper.

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Matrices

☛ A matrix is a rectangular array of numbers arranged in rows and columns.

☛ A matrix is usually denoted by capital letters (e.g., A, B, C).

☛ Each number in a matrix is called an element or entry.


⊙Notation
☛ If a matrix A has m rows and n columns, we write it as Aₘₓₙ (m by n matrix).

✔️ Types of Matrices

☑Row matrix: Only one row (e.g., [2 3 5])

☑Column matrix: Only one column

☑Square matrix: Same number of rows and columns

☑Zero (Null) matrix: All elements are 0

☑Diagonal matrix: Only diagonal elements are non-zero

☑Scalar matrix: Diagonal matrix with same diagonal values

☑Identity matrix (Iₙ): Diagonal = 1, rest = 0

☑Symmetric matrix: A = Aᵗ (transpose)

☑Skew-symmetric matrix: A = -Aᵗ


✔ Matrix Operations

a) Addition and Subtraction

☛ Only possible if matrices have same order

☛ Add/subtract corresponding elements


b) Scalar Multiplication

☛ Multiply each element by a scalar (number)


c) Matrix Multiplication

Multiply Aₘₓₙ × Bₙₓₚ results in Cₘₓₚ

Rule: Multiply row by column

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Transformation on the plane

☛ A transformation of the plane refers to a rule or function that moves or changes the position, size, or orientation of points in the coordinate plane. These transformations are often studied in geometry and linear algebra.

📝There are three main types of transformations in the plane

1. Translation

✔Definition: Slides every point of a figure the same distance in the same direction.

✔Effect: No change in shape, size, or orientation.

Example

(x,y) → (x + a, y + b)

✅where a and b are constants.

2. Rotation

✔Definition: Turns a figure around a fixed point (called the center of rotation) by a certain angle.

✔Effect: Shape and size stay the same, but orientation changes.

🎱Common Rotations

90° counterclockwise: (x, y) → (-y, x)

180°: (x, y) → (-x,-y)

270° counterclockwise: (x, y) → (у, -x)

3. Reflection

✔️Definition: Flips a figure over a line (like a mirror).

🎱Common Reflections

✅Over the x-axis: (x, y) → (x, -y)

✅Over the y-axis: (x, y) → (-x, y)

✅Over the line y = x: (x,y) (y, x)


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Questions 1(English)

Yabsera____ all her classmates at her party but only a few turned up.

A. is expected
B. expected
C. has expected
D. expects

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