docs/sph3u7.md

@@ -18,6 +18,10 @@ Every other SI unit is derived from the fundamental SI units. Memorise these!
 | Amount of substance | Mole | mol |
 | Luminous intensity | Candela | cd |
 
+!!! info "Reminder"
+    Note that on an assesment, you are expected to derive the SI unit expression given the equation of unit.
+    For example Force = mass x acceleration = mass x distance / time / time = $kg \times m \times s^{-2}$. 
+
 ### Metric prefixes
 
 Every SI unit can be expanded with metric prefixes.
@@ -36,6 +40,9 @@ Every SI unit can be expanded with metric prefixes.
 | peta- | P | $10^{15}$ | f | femto- |
 | exa- | E | $10^{18}$ | a | atto- |
 
+!!! note
+    For easier memorization, notice that most of these prefixes are in multiples of $3$. 
+
 ### Significant figures
 
  - The leftmost non-zero digit is the **most significant digit**.
@@ -112,7 +119,7 @@ Uncertainties are stated in the form of [value] ± [uncertainty]. A value is onl
 To determine a measurement's absolute uncertainty, if:
 
  - the instrument states its uncertainty, use that.
- - an analog instrument is used, the last digit is estimated and appended to the end of the reported value. The estimated digit is uncertain by 5 at its order of magnitude.
+ - an analog instrument is used, the uncertainty is half of the smallest scale.
  - a digital instrument is used, the last reported digit is uncertain by 1 at its order of magnitude.
 
 !!! example
@@ -142,9 +149,9 @@ Error bars represent the uncertainty of the data, typically representing that da
 <img src="/resources/images/error-slopes.png" width=700>(Source: Kognity)</img>
 
 The uncertainty of the **slope** of the line of best fit is the difference between the maximum and minimum slopes.
-$$m_{best fit} ± m_{max}-m_{min}$$
+$$m_{\text{best fit}} ± \frac{m_{\max}-m_{\min}}{2}$$
 The uncertainty of the **intercepts** is the difference between the intercepts of the maximum and minimum lines.
-$$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
+$$\text{intercept}_{\text{best fit}} ± \frac{\text{intercept}_{\max} - \text{intercept} _{\min}}{2}$$
 
 
 ## 1.3 - Vectors and scalars
@@ -152,6 +159,7 @@ $$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
 !!! note "Definition"
     - **Scalar:** A physical quantity with a numerical value (magnitude) and a unit.
     - **Vector:** A physical quantity with a numerical value (magnitude), a unit, and a **direction.**
+        - The **minimum magnitude** for any vector must be $`\ge 0`$
 
 ??? example
     - Scalar quantities include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more.
@@ -166,6 +174,7 @@ $$\vec{a} = (1, 1)$$
  - The **magnitude** of a vector can be expressed as the absolute value of a vector.
 $$|\vec{a}| = 1 \text{ m}$$
 
+
 ### Adding/subtracting vectors diagrammatically
 
 1. Draw the first vector.
@@ -179,6 +188,9 @@ When subtracting a vector, **negate** the vector being subtracted by giving it a
 
 <img src="/resources/images/vector-subtract-direction.png" width=700>(Source: Kognity)</img>
 
+!!! note
+    Notice that when we are subtracting vectors ($\vec{a} - \vec{b}$), we have **tail** to **tail** and the difference vector has a direction from ($\vec{b} to \vec{a}$)
+
 ### Adding/subtracting vectors algebraically
 
 Vectors can be broken up into two vectors (**"components"**) laying on the x- and y-axes via trigonometry such that the resultant of the two components is the original vector. This is especially helpful when adding larger (3+) numbers of vectors.