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Sarah derives the standard plane transformation matrices from a single idea, that the columns of a matrix are the images of the unit vectors. She builds anticlockwise rotation through theta, reflection in the line y equals x tan theta with its doubled angle, enlargement as k times the identity, and the two factor stretch. Two worked problems identify a reflection from its matrix and construct a clockwise sixty degree rotation, using the determinant as a check.

Lesson 91 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell teaches calcium, magnesium, and phosphorus through one rule: low is tight, high is tired. She covers hypocalcemia after thyroidectomy with Trousseau's and Chvostek's signs, laryngospasm, and slow IV calcium gluconate; hypercalcemia from hyperparathyroidism and cancer treated with saline, furosemide, calcitonin, and mobility; magnesium toxicity with lost reflexes and its calcium gluconate antidote; phosphorus as calcium's mirror in renal failure and refeeding; plus diet teaching and a reflex and ECG comparison.

Lesson 91 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Lesson ninety builds the two by two inverse as one over a d minus b c times the adjugate, the swap-and-negate matrix, and fixes the singular condition when that determinant is zero. It drills the identity check, the correct side for pre-multiplying and post-multiplying in matrix equations, the reversed-order rule for the inverse of a product, and verification that two given three by three matrices are inverses.

Lesson 90 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell covers the electrolyte the NCLEX tests most. She explains the 3.5 to 5.0 range, why insulin, albuterol, and alkalosis lower serum potassium while acidosis raises it, and the causes, symptoms, and ECG changes of hypokalemia and hyperkalemia. She walks through the IV potassium safety rules, the protect-shift-remove sequence for hyperkalemia, high-potassium foods, the salt substitute trap, and pseudohyperkalemia from hemolyzed samples, with two worked exam scenarios.

Lesson 90 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Sarah works through matrix multiplication for MATSEC Paper One. She sets the conformability rule that the columns of the left matrix must match the rows of the right, shows how each entry is built from a row and a column, and separates the rules that survive from those that fail. Associativity and two-sided distributivity hold. Commutativity and cancellation do not. Two worked two by two products make the point.

Lesson 89 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell frames sodium as a water problem the brain keeps score of. She sorts hyponatremia by volume status, from SIADH and thiazides to heart failure, matches each to isotonic saline, fluid restriction, or three percent saline for severe symptoms, and explains why correction is capped near eight to ten milliequivalents per liter a day. Hypernatremia, slow water replacement, SIADH versus diabetes insipidus, seizure precautions, and two worked scenarios round it out.

Lesson 89 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Lesson 88 sets up the language of matrices for MATSEC Paper One. It defines order as rows before columns and entry labels such as a two one, then shows how matrix equality forces a set of simultaneous equations. It covers entry by entry addition and subtraction under identical order, scalar multiplication, and the square, zero, identity and diagonal matrices, closing with the commutative and associative laws for addition.

Lesson 88 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell maps the fluid compartments, third spacing, and the daily weight rule of one kilogram per liter, then contrasts hypovolemia, fast, flat, dry, and dark, with hypervolemia, wet lungs, bounding pulse, and weight gain. She sorts isotonic, hypotonic, and hypertonic fluids by where the water goes, explains why D5W acts hypotonic, covers fluids for DKA, burns, and hyponatremia, intake and output, specific gravity, and dehydration in infants and older adults.

Lesson 88 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Lesson 87 shows that the angle between two lines depends only on their direction vectors, never on the points they pass through. It covers the cosine formula with scalar product over the product of moduli, the convention of reporting the acute angle, the zero scalar product test for perpendicularity including skew lines, parallel directions as scalar multiples, and solving for a missing component.

Lesson 87 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell walks through every tube the NCLEX tests: reading a chest drainage system, with tidaling normal and continuous water seal bubbling an air leak, plus the disconnection and pull-out emergencies. She covers nasogastric insertion and pH verification, the Salem sump pigtail, sterile tracheostomy suctioning in 10 to 15 second passes, Jackson Pratt, Hemovac, Penrose, and T tube drains, wound vacs, and the rule to assess the patient before the alarm.

Lesson 87 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Lesson 86 teaches the scalar product of vectors in component form, its geometric definition as the product of magnitudes times the cosine of the angle, and the angle formula. It covers the sign test for acute, obtuse and perpendicular, commutativity and distributivity, the result that a dot a equals the magnitude squared, and the requirement that both vectors point away from the shared vertex.

Lesson 86 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell walks the postoperative timeline, airway and positioning in the PACU, the Aldrete score, and discharge criteria, then the complications by the clock, hemorrhage in the first 24 hours with tachycardia before hypotension, atelectasis at 48 hours, DVT and pulmonary embolism, wound infection and dehiscence with evisceration, paralytic ileus, and urinary retention with a bladder scan at 6 to 8 hours. She closes with layered pain management, ambulation, and discharge teaching, plus an early hemorrhage scenario and an evisceration scenario.

Lesson 86 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Sarah shows how to test two lines in three dimensions for a common point by writing one with parameter lambda and the other with mu, equating position vectors, and comparing components to get three equations in two unknowns. Solving two and testing the third decides the case. Two worked examples give an intersection at three, four, five and a skew pair.

Lesson 85 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell walks through the preoperative assessment, latex allergy risk groups, which medications to hold or continue, current fasting guidance, and the preop checklist from consent to site marking to the time out. She covers coughing, spirometer, and leg exercise teaching, preoperative medications, malignant hyperthermia and dantrolene, anesthesia types with ASA classes, circulating and scrub nurse roles, surgical counts, positioning injuries, and special populations, with a consent scenario and a medication hold scenario.

Lesson 85 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Lesson 84 builds the equation of a straight line in three dimensions from a point and a direction. It derives r equals a plus lambda d, reads off the parametric components, eliminates lambda to reach the Cartesian chain of fractions, and handles a zero direction component. It also reads Cartesian form backwards, stresses that line equations are not unique, and tests two lines for parallel versus identical.

Lesson 84 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell covers the nursing care around common diagnostic tests, including the shellfish and iodine myth, holding metformin for 48 hours after contrast, MRI metal screening, cardiac catheterization site and pulse checks, gag reflex return after bronchoscopy and endoscopy, bowel prep and barium care, and positioning and complications for lumbar puncture, paracentesis, thoracentesis, liver biopsy, and bone marrow biopsy. She closes with consent, time outs, and moderate sedation monitoring, plus a retroperitoneal bleed scenario and a post bronchoscopy scenario.

Lesson 84 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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This lesson separates a vector's length from its direction. Sarah shows that the magnitude of i plus two j minus two k is three, builds the unit vector by dividing by three, and checks it by squaring components to one. She covers position vectors, the finish minus start rule for the vector from A to B, three dimensional distance, scaling a unit vector to a required length, and the reversing minus sign.

Lesson 83 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell teaches pressure injury staging from stage 1 through stage 4, unstageable, and deep tissue injury, the six Braden categories with the 18 or less cutoff, and the prevention bundle. She covers wound measurement, drainage types, healing by primary, secondary, and tertiary intention, dressing selection, wound vac basics, the ABCDE rule, rule of nines, musculoskeletal grading, and neurovascular checks, with a compartment syndrome scenario and a staging scenario.

Lesson 83 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell shows that a vector in i, j, k form and the same vector in column form are one object, then drills component-by-component addition and subtraction, scalar multiplication, the triangle rule, the arrow from the tip of a to the tip of b, the scalar-multiple test for parallel vectors, the zero vector, and the ordinary algebra rules. Two worked problems find a parallel constant and a missing displacement leg.

Lesson 82 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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Sarah Mitchell walks through the abdominal assessment sequence, inspect, auscultate, percuss, palpate, what bowel sound counts mean, and what named signs like Murphy's, McBurney's, Cullen's, and Grey Turner point to, along with stool and emesis colors. She then covers urinary red flags, the output floor, bladder scanning, catheter care, costovertebral angle tenderness, and sexual history taking, with a ruptured appendix scenario and a post catheter urinary retention scenario.

Lesson 82 of 125 in the NCLEX-RN Complete Prep Course audio course from ExamPrepRise.

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