This is a question on interpretation of principal component analysis when the input could be a correlation matrix (standardized variables) or a covariance matrix (no scaling, in which case, pay attention to the units and range of the variables).
A data set consists of women national track records in the year 1984 for over 50 countries: variables are record times for 100m, 200m, 400m in seconds, and for 800m, 1500m, 3000m, marathon (42195m) in minutes.
Your data variables are:

m100=c(12.9, 11.96, 11.61, 11.81, 10.79, 11.2, 11.13, 11.76, 11.45, 11.76, 11.29, 11.13, 12.3, 11.25, 11.84, 11.89, 11.95, 11.79, 11.22, 11.75, 11.01, 12.03, 11.96, 11.8, 11, 11.41, 11.98, 11.55, 11.31, 11.6, 11.46, 10.81, 11.43, 11.06, 12, 11.09, 12.14, 12.25, 11.43, 11.73, 12.74, 11.45, 12.25, 11.15, 11.85, 11.73, 11.45, 11.16, 11.58, 11.42, 11, 12.23, 11.95, 11.79)

m200=c(27.1, 24.49, 22.94, 24.22, 21.83, 22.35, 22.39, 23.54, 23.57, 25.08, 23, 22.21, 25, 22.81, 24.54, 23.62, 24.28, 24.05, 22.62, 24.46, 22.39, 24.96, 24.6, 23.98, 22.25, 23.04, 24.44, 23.13, 23.17, 24, 23.05, 21.71, 23.51, 22.19, 24.52, 21.97, 24.47, 25.07, 23.09, 24, 25.85, 23.31, 25.78, 22.59, 24.24, 23.88, 23.06, 22.82, 23.31, 23.52, 22.13, 24.21, 24.41, 24.08)

m400=c(60.4, 55.7, 54.5, 54.3, 50.62, 51.08, 50.14, 54.6, 54.9, 58.1, 52.01, 49.29, 55.08, 52.38, 56.09, 53.76, 53.6, 56.05, 52.5, 55.8, 49.75, 56.1, 58.25, 53.59, 50.06, 52, 56.45, 51.6, 52.8, 53.26, 53.3, 48.16, 53.24, 49.19, 54.9, 47.99, 55, 56.96, 50.62, 53.73, 58.73, 53.11, 51.2, 51.73, 55.34, 52.7, 51.5, 51.79, 53.12, 53.6, 50.46, 55.09, 54.97, 54.93)

m800=c(2.3, 2.15, 2.15, 2.09, 1.96, 1.98, 2.03, 2.19, 2.1, 2.27, 1.96, 1.95, 2.12, 1.99, 2.28, 2.04, 2.1, 2.24, 2.1, 2.2, 1.95, 2.07, 2.21, 2.05, 2, 2, 2.15, 2.02, 2.1, 2.11, 2.16, 1.93, 2.05, 1.89, 2.05, 1.89, 2.18, 2.24, 1.99, 2.09, 2.33, 2.02, 1.97, 2, 2.22, 2, 2.01, 2.02, 2.03, 2.03, 1.98, 2.19, 2.08, 2.07)

m1500=c(4.84, 4.42, 4.43, 4.16, 3.95, 4.13, 4.1, 4.6, 4.25, 4.79, 3.98, 3.99, 4.52, 4.06, 4.86, 4.25, 4.32, 4.74, 4.38, 4.72, 4.03, 4.38, 4.68, 4.14, 4.06, 4.14, 4.37, 4.18, 4.49, 4.35, 4.58, 3.96, 4.11, 3.87, 4.23, 4.14, 4.45, 4.84, 4.22, 4.35, 5.81, 4.07, 4.25, 4.14, 4.61, 4.15, 4.14, 4.12, 4.01, 4.18, 4.03, 4.69, 4.33, 4.35)

m3000=c(11.1, 9.62, 9.79, 8.84, 8.5, 9.08, 8.92, 10.16, 9.37, 10.9, 8.63, 8.97, 9.94, 9.01, 10.54, 9.59, 9.98, 9.89, 9.63, 10.28, 8.59, 9.64, 10.43, 9.02, 8.81, 8.88, 9.38, 8.76, 9.77, 9.46, 9.81, 8.75, 8.89, 8.45, 9.37, 8.92, 9.51, 10.69, 9.34, 9.2, 13.04, 8.77, 9.35, 8.98, 10.02, 9.2, 8.98, 8.84, 8.53, 8.71, 8.62, 10.46, 9.31, 9.87)

marathon=c(233.22, 164.65, 178.52, 151.2, 142.72, 152.37, 154.23, 200.37, 160.48, 261.13, 151.82, 160.82, 182.77, 152.48, 215.08, 158.53, 188.03, 203.88, 177.87, 168.45, 148.53, 174.68, 171.8, 162.6, 149.45, 157.85, 201.08, 145.48, 168.75, 165.42, 169.98, 157.68, 149.38, 151.22, 171.38, 158.85, 191.02, 233, 159.37, 150.5, 306, 153.42, 179.17, 155.27, 201.28, 181.05, 156.37, 154.48, 145.48, 151.75, 149.72, 182.17, 168.48, 182.2)

country=c('cookis', 'korea', 'argentin', 'portugal', 'usa', 'australi', 'finland', 'philippi', 'israel', 'mauritiu', 'italy', 'poland', 'singapor', 'netherla', 'guatemal', 'mexico', 'india', 'domrep', 'taipei', 'thailand', 'frg', 'luxembou', 'costa', 'spain', 'canada', 'belgium', 'turkey', 'nz', 'brazil', 'columbia', 'bermuda', 'gdr', 'ireland', 'ussr', 'chile', 'czech', 'burma', 'png', 'austria', 'japan', 'wsamoa', 'switzerl', 'dprkorea', 'france', 'indonesi', 'kenya', 'hungary', 'sweden', 'norway', 'denmark', 'gbni', 'malaysia', 'china', 'greece')

Make a data.frame with
track=data.frame(m100,m200,m400,m800,m1500,m3000,marathon)

Principal component analysis is to be applied using both the sample covariance and sample correlation matrix of the data as given, also principal component analysis is applied to the velocity or speed data (with unit of m/s).
To convert a record time in seconds to m/s, take the distance in metres and divide by the record time.
To convert a record time in minutes to m/s, take the distance in metres and divide by the record time and then divide by 60.
For the interpretation questions, you may want to plot the scores of the first two principal components with an abbreviated country name as a plotting symbol.

Part a)
The number of principal components to achieve 90% of the variation is
for the covariance matrix of record times
for the correlation matrix of record times
for the covariance matrix of velocities

Part b)
The absolute value of the coefficient of marathon in the first principal component is:
for the covariance matrix of record times
for the correlation matrix of record times
for the covariance matrix of velocities

Part c)
For the covariance matrix of record times, the interpretation of the first principal component (linear combination with most variation) is:
(There can be more than one correct answer)

A. weighted sum of the variables
B. contrast of long distances versus short distances
C. random weighting
D. contrast of long distances versus medium distances
E. contrast of long and short distances versus medium distances
F. marathon
G. contrast of marathon distances versus other distances
H. None of the above


Part d)
For the correlation matrix of record times, the interpretation of the first principal component is:
(There can be more than one correct answer)

A. contrast of marathon distances versus other distances
B. marathon
C. contrast of long distances versus short distances
D. contrast of long and short distances versus medium distances
E. contrast of long distances versus medium distances
F. weighted sum of the variables
G. random weighting
H. None of the above


Part e)
For the covariance matrix of velocities, the interpretation of the second principal component is:
(There can be more than one correct answer)

A. marathon
B. weighted sum of the variables
C. contrast of long distances versus medium distances
D. contrast of long distances versus short distances
E. contrast of marathon distances versus other distances
F. random weighting
G. contrast of long and short distances versus medium distances
H. None of the above


Part f)
Why is it appropriate to do principal component analysis on the covariance matrix of the velocities but not the covariance matrix of the actual record times.
For the velocity data, which of the following are relevant for principal component analysis? (There can be more than one correct answer)

A. the standard deviations of the 7 variables are about the same
B. units of the variables are the same
C. the variables have the same order of magnitude
D. the values are decreasing in most rows
E. the mean values of the 7 variables are about the same
F. the median values of the 7 variables are about the same
G. None of the above

Hint: