MikaStars39/nano-eval huggingface dataset:
Try to factor the linear transformation $w={\frac{3z+4}{\mathrm{i}z-1}}$ into a combination of four simple (linear) transformations.

Options:
A. $$
z_{1}=z-\mathrm{i}
$$
$$
z_{2}={z_{1}}^{2}
$$
$$
z_{3}=\mid4+3 \mathrm{i} \mid z_{2}=5 z_{2}
$$
$$
z_{4}=\mathrm{e}^{-\mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{3} {4}})
$$
$$
z_{5}=\mathrm{e}^{\mathrm{i} \pi/2} z_{4} \,, w=z_{5}+3 \mathrm{i}
$$
B. $$
z_{1}=z+\mathrm{i}
$$
$$
z_{2}=\frac{1}{\mathrm{i} z_{1}}
$$
$$
z_{3}=\mid3+5 \mathrm{i} \mid z_{2}=5 z_{2}
$$
$$
z_{4}=\mathrm{e}^{-\mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{3} {5}})
$$
$$
z_{5}=\mathrm{e}^{2 \mathrm{i} \pi} z_{4} \,, w=z_{5}-3 \mathrm{i}
$$
C. $$
z_{1}=z-2
$$
$$
z_{2}=z_{1}^{2}
$$
$$
z_{3}=\mid5+4 \mathrm{i} \mid z_{2}=6 z_{2}
$$
$$
z_{4}=\mathrm{e}^{3 \mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {5}})
$$
$$
z_{5}=\mathrm{e}^{\mathrm{i} \pi} z_{4} \,, w=z_{5}+3 \mathrm{i}
$$
D. $$
z_{1}=z-\mathrm{i}
$$
$$
z_{2}=\mathrm{i} z_{1}
$$
$$
z_{3}=\mid2+3 \mathrm{i} \mid z_{2}=5 z_{2}
$$
$$
z_{4}=\mathrm{e}^{2 \mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {3}})
$$
$$
z_{5}=\mathrm{e}^{\mathrm{i} \pi} z_{4} \,, w=z_{5}+4 \mathrm{i}
$$
E. $$
z_{1}=z+\mathrm{i}
$$
$$
z_{2}=\frac{1} {z_{1}}
$$
$$
z_{3}=\mid3+4 \mathrm{i} \mid z_{2}=5 z_{2}
$$
$$
z_{4}=\mathrm{e}^{\mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {3}} )
$$
$$
z_{5}=\mathrm{e}^{\mathrm{i} \pi} z_{4} \,, w=z_{5}-3 \mathrm{i}
$$
F. $$
z_{1}=z+2\mathrm{i}
$$
$$
z_{2}=\frac{1} {2z_{1}}
$$
$$
z_{3}=\mid0+4 \mathrm{i} \mid z_{2}=5 z_{2}
$$
$$
z_{4}=\mathrm{e}^{4 \mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {0}})
$$
$$
z_{5}=\mathrm{e}^{\mathrm{i} \pi} z_{4} \,, w=z_{5}+1 \mathrm{i}
$$
G. $$
z_{1}=z+\frac{\mathrm{i}}{4}
$$
$$
z_{2}=\frac{1} {z_{1}}
$$
$$
z_{3}=\mid3+4 \mathrm{i} \mid z_{2}=6 z_{2}
$$
$$
z_{4}=\mathrm{e}^{2 \mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {3}})
$$
$$
z_{5}=\mathrm{e}^{\mathrm{i} \pi} z_{4} \,, w=z_{5}-4 \mathrm{i}
$$
H. $$
z_{1}=z+3\mathrm{i}
$$
$$
z_{2}=\frac{1} {z_{1}}
$$
$$
z_{3}=\mid3+4 \mathrm{i} \mid z_{2}=4 z_{2}
$$
$$
z_{4}=\mathrm{e}^{\mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {3}})
$$
$$
z_{5}=\mathrm{e}^{3 \mathrm{i} \pi} z_{4} \,, w=z_{5}+4 \mathrm{i}
$$
I. $$
z_{1}=z+\frac{\mathrm{i}}{2}
$$
$$
z_{2}=\frac{1} {z_{1}}
$$
$$
z_{3}=\mid4+4 \mathrm{i} \mid z_{2}=5 z_{2}
$$
$$
z_{4}=\mathrm{e}^{2 \mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {2}})
$$
$$
z_{5}=\mathrm{e}^{\mathrm{i} \pi} z_{4} \,, w=z_{5}+3 \mathrm{i}
$$
J. $$
z_{1}=z+2\mathrm{i}
$$
$$
z_{2}=\frac{1} {2z_{1}}
$$
$$
z_{3}=\mid1+4 \mathrm{i} \mid z_{2}=5 z_{2}
$$
$$
z_{4}=\mathrm{e}^{-\mathrm{i}} z_{3} \, ( \alpha=
\operatorname{a r c t a n} {\frac{4} {1}})
$$
$$
z_{5}=\mathrm{e}^{2 \mathrm{i} \pi} z_{4} \,, w=z_{5}-2 \mathrm{i}
$$
Answer: E
The total mass of a rear-wheel-drive vehicle is $2152 \, \text{kg}$. The front axle load is 52%, and the rear axle load is 48%. The main transmission ratio is $i_{O} = 4.55$. The transmission ratios for the gears are as follows: first gear: 3.79; between first and second gear, 2.17; second gear, 1.41; fourth gear, 1.00; fifth gear, 0.86. The height of the center of gravity is $h_{\text{g}} = 0.57\, \text{m}$, and the drag area $CDA = 1.5 \, \text{m}^2$. The wheelbase is $L = 2.300 \, \text{m}$. The rotational inertia of the flywheel is $I_{\text{f}} = \text{kg}\cdot\text{m}^2$. The total rotational inertia of the four wheels is $I_{\text{w}} = 3.6 \, \text{kg}\cdot\text{m}^2$. The wheel radius is $r = 0.367 \, \text{m}$. The vehicle's low-speed coasting curve and direct gear acceleration curve on a road surface with an adhesion coefficient $\psi = 0.6$ are shown in Figure 1 of the exercise problem. The fitting line of the coasting data given is $\nu = 19.76 - 0.59T$, where $\nu$ is in $\text{km/h}$ and $T$ is in seconds. The maximum acceleration in direct gear is $\alpha_{\text{max}} = 0.75 \, \text{m/s}^2$ (at $u_s = 50 \, \text{km/h}$). Assuming the transmission efficiency for each gear is 0.90, determine the vehicle's maximum gradient on this road surface.

Options:
A. $$
= 1 5. 0 2^{\circ}
$$
B. $$
= 1 1. 9 8^{\circ}
$$
C. $$
= 1 7. 5 0^{\circ}
$$
D. $$
= 1 6. 4 1^{\circ}
$$
E. $$
= 1 0. 7 9^{\circ}
$$
F. $$
= 1 2. 3 5^{\circ}
$$
G. $$
= 1 4. 8 5^{\circ}
$$
H. $$
= 1 3. 4 6^{\circ}
$$
I. $$
= 1 8. 3 7^{\circ}
$$
J. $$
= 1 9. 2 8^{\circ}
$$
Answer: D
To determine the land price by the land surplus method, we first calculate the total net income (property price) _____, and then deduct the income of buildings from it to obtain the net income of land, and then use the interest rate to restore the land price.

Options:
A. Value of depreciated assets
B. Estimate from market trends
C. Land and buildings
D. Assessment of development risks
E. Value from land surveys
F. Appraisal of infrastructure fees
G. Income from rentals
H. Projection from equity gains
I. Total construction cost
J. Forecast from future rents
Answer: C
Channel engineering includes () and () two sections.

Options:
A. River/Construction of Bridges
B. Tributary/Creation of Tanks
C. Canal/System of Canal Structures
D. Reservoir/Building of Canals
E. Riverbed/Construction of Locks
F. Channel/Formation of Reservoirs
G. Waterway/System of Water Barriers
H. Stream/Formation of Dams
I. Aqueduct/Formation of Rivers
J. Stream/System of Watercourses
Answer: C
A light source S and a receiver $\mathrm{R}$ are stationary relative to each other, with a distance of $l_{0}$ between them. The S-R device is immersed in a uniform, infinite liquid medium (with a static refractive index of $n$). Calculate the time taken for the signal emitted by the light source to reach the receiver in the following three scenarios:
The liquid medium is stationary relative to the S-R device; the liquid flows along the $\mathrm{S-R}$ line at a velocity $\mathcal{V}$ of $v$; the liquid flows perpendicular to the S-R line at a velocity $v$.

Options:
A. $$
\frac{n l_{0}} {c}
$$
$$
\frac{\left( 1+v / n c \right) l_{0}} {c / n+v}
$$
$$
\frac{l_{0} \sqrt{1-v^{2} / c^{2}}} {\sqrt{c^{2} / n^{2}-v^{2}}}
$$
B. $$
\frac{l_{0} c}{n}
$$
$$
\frac{\left( 1-n v / c \right) l_{0}}{n c+v}
$$
$$
\frac{l_{0} \sqrt{1-v^{2} / n^2 c^{2}}}{\sqrt{c-v^2 n^{2} / c}}
$$
C. $$
\frac{n^3 l_{0}}{c^2}
$$
$$
\frac{\left( 1/ c+v n \right) l_{0}}{c-n v}
$$
$$
\frac{l_{0} \sqrt{1-v^{2} / n^2 c}}{\sqrt{c^{2}/n^2-v^2}}
$$
D. $$
\frac{l_{0} c}{n^2}
$$
$$
\frac{\left( 1-v / c n \right) l_{0}}{n c - v}
$$
$$
\frac{l_{0} \sqrt{1-n v^{2} / c^{2}}}{\sqrt{c^{2}/ n+ v^2}}
$$
E. $$
\frac{l_{0}}{c n}
$$
$$
\frac{\left( nv +1 / c \right) l_{0}}{c n+v}
$$
$$
\frac{l_{0} \sqrt{1+v^{2} / c^{2}}}{\sqrt{c^{2} n^2-v^{2}}}
$$
F. $$
\frac{n l_{0}^2}{c}
$$
$$
\frac{\left( n+v / c \right) l_{0}}{c - n v}
$$
$$
\frac{l_{0} \sqrt{1 - v^{2} / c^{2} n^2}}{\sqrt{c^2+v^2 n}}
$$
G. $$
\frac{l_{0}}{n^2 c}
$$
$$
\frac{n \left( 1-v / c \right) l_{0}}{c+nv}
$$
$$
\frac{l_{0} \sqrt{1+v^{2} / n^{2} c^{2}}}{\sqrt{c^{2}-n^{2} v^{2}}}
$$
H. $$
\frac{l_{0}}{c}
$$
$$
\frac{\left( 1+n v / c \right) l_{0}}{c v + n}
$$
$$
\frac{l_{0} \sqrt{1+c v^{2} / n^{2}}}{\sqrt{c^2 / n^2+v^{2}}}
$$
I. $$
\frac{n^2 l_{0}}{c^2}
$$
$$
\frac{\left( 1-v n / c \right) l_{0}}{c+n v}
$$
$$
\frac{l_{0} \sqrt{1-v^{2} / c^{2} n}}{\sqrt{c^{2}/ n-v^2}}
$$
J. $$
\frac{l_{0} n}{c^2}
$$
$$
\frac{\left( 1+ v n / c \right) l_{0}}{c-v}
$$
$$
\frac{l_{0} \sqrt{1-n^2 v^{2} / c^{2}}}{\sqrt{c^2-n v^{2}}}
$$
Answer: A
What is the developmental sequence of polyphonic music?

Options:
A. Gregorian Chant-Clausula-Discant-Organum
B. Discant-Organum-Clausula-Gregorian Chant
C. Discant-Clausula-Organum-Gregorian Chant
D. Organum-Gregorian Chant-Clausula-Discant
E. Clausula-Gregorian Chant-Discant-Organum
F. Organum-Discant-Gregorian Chant-Clausula
G. Gregorian Chant-Discant-Clausula-Organum
H. Organum-Clausula-Gregorian Chant-Discant
I. Clausula-Discant-Organum-Gregorian Chant
J. Discant-Gregorian Chant-Organum-Clausula
Answer: E
Into which two types can 18th-century German singspiels be divided?

Options:
A. Hamburg Operas and Tyrolean Songs
B. Leipzig Opera and Vienna Opera
C. Cologne Divertissements and Austrian Operas
D. Leipzig Operettas and Prussian Anthems
E. Württemberg Arias and Berlin Operettas
F. Dresden Dramas and Berlin Cantatas
G. Frankfurt Arias and Bavarian Operettas
H. Vienna Waltzes and Saxon Singspiels
I. Munich Operas and Hamburg Plays
J. Danish Cantatas and Berliner Musicals
Answer: B
Which musical school made a significant contribution to the development of sonata during the Baroque period?

Options:
A. Salzburg School
B. Bologna School
C. Florentine School
D. Leipzig School
E. Vienna School
F. Dresden School
G. Neapolitan School
H. Venetian School
I. Prague School
J. Parisian School
Answer: B
In which opera by Richard Strauss do dissonant tones and nearly atonal harmonies perfectly align with the cruel plot, earning it the title of a "horror opera"?

Options:
A. "Ariadne auf Naxos"
B. "Guntram"
C. "Der Rosenkavalier"
D. "Die Frau ohne Schatten"
E. "Electra"
F. "Salome"
G. "Intermezzo"
H. "Capriccio"
I. "Arabella"
J. "Feuersnot"
Answer: E
Which of Puccini's works fall under operas with a realistic tendency?

Options:
A. "Turandot"; "La Traviata"; "La Rondine".
B. "Carmen"; "Il Tabarro"; "La Cenerentola".
C. "Carmen"; "Il Trovatore"; "La Fanciulla del West".
D. "La Traviata"; "Rigoletto"; "Norma".
E. "Tosca"; "La Vie de Bohème"; "La Bohème".
F. "Don Giovanni"; "La Cenerentola"; "La Rondine".
G. "Madama Butterfly"; "Don Giovanni"; "Pagliacci".
H. "Norma"; "Turandot"; "Il Trovatore".
I. "Manon"; "Rinaldo"; "Madama Butterfly".
J. "Turandot"; "Manon Lescaut"; "La Fanciulla del West".
Answer: E
What are the characteristics of Neoclassical music?

Options:
A. Introduce electronic instruments and synthesized sounds; exploring new timbres.
B. Incorporate folk melodies into chromatic harmonies; adding irregular rhythms.
C. Embrace dissonant harmonies and atonal structures; avoiding classical forms.
D. Develop complex polyphonic textures; inspired by modern experimental styles.
E. Highlight extreme dynamic contrasts and rapid tempo changes; rejecting tradition.
F. Utilize serialist techniques with strict tone rows; replacing tonal stability.
G. Emphasize programmatic content and narrative storytelling; favoring Romantic ideals.
H. Focus on blending Romantic lushness with Baroque counterpoint; emphasizing emotion.
I. Replace the chromatic harmony of late Romanticism with natural scales; lacking harmonic function.
J. Prioritize improvisational freedom and extended techniques; avoiding formal constraints.
Answer: I
What is the format of the combat competitive event group competition ?

Options:
A. One-on-one confrontation
B. Random combat pairings
C. Collaborative skill demonstrations
D. Randomized group showdowns
E. Cooperative group exercises
F. Turn-based point sparring
G. Friendly rivalry exchanges
H. Individual freestyle routines
I. Simultaneous team face-offs
J. Multi-team elimination rounds
Answer: A
A star is observed to cross the meridian (due south) at an elevation of $3 4^{\circ}$ , as seen from an observatory sited at a latitude of 42° north. At the moment of transit, a clock running on Universal Time (UT) read $\mathrm{03 h 16 min 24s}$. At the previous midnight, the sidereal time was $\mathrm{14 h 38 min 54s}$. What is the Right Ascension of the star?

Options:
A. $\mathrm{14 h 33 min 50s}$
B. $\mathrm{21 h 22 min 05s}$
C. $\mathrm{15 h 55 min 45s}$
D. $\mathrm{12 h 58 min 37s}$
E. $\mathrm{16 h 42 min 38s}$
F. $\mathrm{18 h 20 min 15s}$
G. $\mathrm{19 h 10 min 24s}$
H. $\mathrm{13 h 48 min 12s}$
I. $\mathrm{20 h 05 min 16s}$
J. $\mathrm{17 h 55 min 50s}$
Answer: J
A planet lies at a distance of $3 \times1 0^{1 1}$ m from the central star of its solar system. The solar constant is measured to be $280 \mathbf{Wm}^{-2}$ . The angular diameter of the star, as measured from the planet, is 22 arcmin. Estimate the surface temperature of the star.

Options:
A. $$
4. 0 2 \times1 0^{3} \mathrm{K}
$$
B. $$
4. 6 9 \times1 0^{3} \mathrm{K}
$$
C. $$
4. 3 5 \times1 0^{3} \mathrm{K}
$$
D. $$
6. 0 7 \times1 0^{3} \mathrm{K}
$$
E. $$
6. 1 3 \times1 0^{3} \mathrm{K}
$$
F. $$
5. 7 4 \times1 0^{3} \mathrm{K}
$$
G. $$
3. 9 6 \times1 0^{3} \mathrm{K}
$$
H. $$
5. 2 8 \times1 0^{3} \mathrm{K}
$$
I. $$
3. 5 8 \times1 0^{3} \mathrm{K}
$$
J. $$
4. 8 2 \times1 0^{3} \mathrm{K}
$$
Answer: B
Whilst Venus was making its closest approach to Earth, a Doppler radar, transmitting at a frequency of 1420 MHz, received an echo from Venus which was spread' over a bandwidth of 17.1 Hz. Calculate the speed at which the receding limb is travelling away from us with respect to the centre of Venus and hence estimate, in Earth days, how long Venus takes to make one rotation about its axis ? (Assume the velocity of light is $3 \times1 0^ 5 \, \mathrm{k m \cdot s^{-1}}$ . The non-relativistic Doppler formula is given by $\Delta f / f=\Delta v / c$ . Venus has a diameter of
12 104 km.)

Options:
A. $$\mathrm{2.2 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.90years}$$
B. $$\mathrm{1.4 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.55years}$$
C. $$\mathrm{1.5 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.60years}$$
D. $$\mathrm{1.9 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.85years}$$
E. $$\mathrm{2.1 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.80years}$$
F. $$\mathrm{2.0 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.75years}$$
G. $$\mathrm{1.8 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.66years}$$
H. $$\mathrm{1.7 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.70years}$$
I. $$\mathrm{1.6 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.65years}$$
J. $$\mathrm{2.3 \times 10^{-3}km \cdot s^{-1}}$$
$$\mathrm{0.95years}$$
Answer: G
A telescope of 1000 mm focal length is provided with 32 and 11 mm Plossl eyepieces along with a $\times 2$ Barlow lens. The 32 and 11 mm eyepieces have field stop diameters of 27 mm and 9 mm, respectively. What fields of view would be observed with these two eyepieces?

Options:
A. $$
0.6102^{0}
$$
$$
0.2297^{0}
$$
B. $$
0.7984^{0}
$$
$$
0.2764^{0}
$$
C. $$
0.8432^{0}
$$
$$
0.3125^{0}
$$
D. $$
1.0321^{0}
$$
$$
0.4018^{0}
$$
E. $$
0.9127^{0}
$$
$$
0.3156^{0}
$$
F. $$
0.8876^{0}
$$
$$
0.3002^{0}
$$
G. $$
0.5523^{0}
$$
$$
0.2108^{0}
$$
H. $$
0.9713^{0}
$$
$$
0.3485^{0}
$$
I. $$
0. 7 7 3 5 5^{0}
$$
$$
0.2579^{0}
$$
J. $$
0.6834^{0}
$$
$$
0.2932^{0}
$$
Answer: I
What would the resolution be of the Square Kilometre Array when operating at 21 cm wavelength using baselines out to 2000 km?

Options:
A. $$
3. 4 \times1 0^{-2} \mathrm{a r c s e c}
$$
B. $$
2. 9 \times1 0^{-2} \mathrm{a r c s e c}
$$
C. $$
2. 0 \times1 0^{-2} \mathrm{a r c s e c}
$$
D. $$
4. 3 \times1 0^{-2} \mathrm{a r c s e c}
$$
E. $$
2. 6 \times1 0^{-2} \mathrm{a r c s e c}
$$
F. $$
2. 2 \times1 0^{-2} \mathrm{a r c s e c}
$$
G. $$
1. 8 \times1 0^{-2} \mathrm{a r c s e c}
$$
H. $$
5. 0 \times1 0^{-2} \mathrm{a r c s e c}
$$
I. $$
3. 9 \times1 0^{-2} \mathrm{a r c s e c}
$$
J. $$
6. 1 \times1 0^{-2} \mathrm{a r c s e c}
$$
Answer: E
A circular planetary nebula has an angular size of 2 arcmin and lies at a distance of ~600 pc. Doppler shift measurements show that the gaseous shell is expanding at a rate of $20 \mathrm{km \cdot s}^{-1}$ . How long ago was the planetary nebula formed?

Options:
A. $$
5. 7 \times1 0^{3} \mathrm{y e a r s}
$$
B. $$
2. 5 \times1 0^{4} \mathrm{y e a r s}
$$
C. $$
8. 5 \times1 0^{3} \mathrm{y e a r s}
$$
D. $$
1. 8 \times1 0^{4} \mathrm{y e a r s}
$$
E. $$
4. 9 \times1 0^{3} \mathrm{y e a r s}
$$
F. $$
3. 6 \times1 0^{3} \mathrm{y e a r s}
$$
G. $$
7. 2 \times1 0^{3} \mathrm{y e a r s}
$$
H. $$
1. 2 \times1 0^{4} \mathrm{y e a r s}
$$
I. $$
9. 8 \times1 0^{3} \mathrm{y e a r s}
$$
J. $$
6. 4 \times1 0^{3} \mathrm{y e a r s}
$$
Answer: C
Observations of the central region of the Galaxy M87 indicate that stars which are 60 light years from the centre are orbiting the central super-massive black hole at a speed of $\mathbf{550 km \cdot s}^{-1}$ . Estimate the mass of the black hole in solar masses. (The Earth orbits the Sun with an orbital speed of $\mathbf{30 km \cdot s}^{-1}$. 1 light year is 63240 AU.)

Options:
A. $$
3. 7 \times 10^{8} M_{\odot}
$$
B. $$
6. 3 \times 10^{8} M_{\odot}
$$
C. $$
7. 1 \times 10^{8} M_{\odot}
$$
D. $$
1. 9 \times 10^{7} M_{\odot}
$$
E. $$
1. 3 \times1 0^{9} M_{\odot}
$$
F. $$
4. 5 \times 10^{9} M_{\odot}
$$
G. $$
2. 8 \times 10^{9} M_{\odot}
$$
H. $$
2. 1 \times 10^{10} M_{\odot}
$$
I. $$
9. 4 \times 10^{8} M_{\odot}
$$
J. $$
5. 2 \times 10^{9} M_{\odot}
$$
Answer: E
The energy of the $\mathbf{X}$-ray photon is 0.41 MeV. When it collides with a stationary free electron, the recoil electron's velocity is 0.6 times the speed of light. What is the scattering angle?

Options:
A. 85°
B. 51°
C. 64°
D. 78°
E. 39°
F. 58°
G. 67°
H. 95°
I. 72°
J. 45°
Answer: C
What is the wavenumber difference between the maximum and minimum spectroscopic term values for a hydrogen atom, a singly ionized helium ion, and a doubly ionized lithium ion in the state with the principal quantum number $n = 3$?

Options:
A. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.132\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.21 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=10.6\mathrm{cm}^{-1}.$$
B. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.152\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.45 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=12.3\mathrm{cm}^{-1}.$$
C. $$
\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.144\mathrm{cm}^{-1},
\Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.31 \mathrm{cm}^{-1},
\Delta\widetilde{\nu}_{\mathrm{L}^{++}}=11.7\mathrm{cm}^{-1}.
$$
D. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.150\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.52 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=11.9\mathrm{cm}^{-1}.$$
E. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.136\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.41 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=12.5\mathrm{cm}^{-1}.$$
F. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.140\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.28 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=10.9\mathrm{cm}^{-1}.$$
G. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.165\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.37 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=12.0\mathrm{cm}^{-1}.$$
H. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.148\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.56 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=13.1\mathrm{cm}^{-1}.$$
I. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.157\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.33 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=11.1\mathrm{cm}^{-1}.$$
J. $$\Delta\widetilde{\nu}_{\mathrm{H}}\approx0.122\mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{He}^{+}}=2.14 \mathrm{cm}^{-1}, \Delta\widetilde{\nu}_{\mathrm{L}^{++}}=11.4\mathrm{cm}^{-1}.$$
Answer: C
The shortest absorption edges of Ag (Z=47) atoms are 0.0485 nm, 0.324 nm, 0.351 nm, and 0.369 nm, respectively. What is the longest wavelength of the $K$-series lines of Ag?

Options:
A. $$
0.447{\AA}
$$
B. $$
0.728{\AA}
$$
C. $$
0.654{\AA}
$$
D. $$
0.589{\AA}
$$
E. $$
0.391{\AA}
$$
F. $$
0.432{\AA}
$$
G. $$
0.502{\AA}
$$
H. $$
0.784{\AA}
$$
I. $$
0.619{\AA}
$$
J. $$
0.563{\AA}
$$
Answer: J
The electronic configuration 2p3d can form $^3 {\bf D}_{3, \mathrm{2, \mathrm{1}}}$, and 2s2p can form $^3 \mathrm{P}_{2, ~ 1, ~ 0}, ~ ~^{3} \mathrm{D}_{3, ~ 2, ~ 1} \to^{3} \mathrm{P}_{2, ~ 1,0}$ . How many spectral lines are produced by electric dipole radiation transitions?

Options:
A. 3
B. 2
C. 1
D. 8
E. 9
F. 0
G. 5
H. 6
I. 7
J. 4
Answer: F
What is the vibrational energy level spacing of a hydrogen molecule ($H_{2}$) with a force constant of $k = 35.5 eV / \dot{A}^{2}$?

Options:
A. $$
0.530eV
$$
B. $$
0.658eV
$$
C. $$
0.542eV
$$
D. $$
0.495eV
$$
E. $$
0.610eV
$$
F. $$
0.590eV
$$
G. $$
0.712eV
$$
H. $$
0.625eV
$$
I. $$
0.483eV
$$
J. $$
0.478eV
$$
Answer: C
What is the component of the electron spin magnetic moment?

Options:
A. $$
\sqrt{3} h
$$
B. $$
\frac{3} {2} h
$$
C. $$
{\sqrt{3}}{\mu}_s
$$
D. $$
\frac{1} {\sqrt{3}} h
$$
E. $$
\frac{1} {\sqrt{2}} \mu_s
$$
F. $$
2 \mu_s
$$
G. $$
\frac{1} {2}\sqrt{3} h
$$
H. $$
\frac{1} {2} h
$$
I. $$
\frac{\sqrt{2}} {3} \mu_s
$$
J. $$
{\mu}_s
$$
Answer: J
When a certain atom is in the quintet state $^{5}F$, the total magnetic moment is 0. What is its total angular momentum quantum number?

Options:
A. 3
B. 5/2
C. 0
D. 4
E. 6
F. 7/2
G. 3/2
H. 1/2
I. 1
J. 2
Answer: I
CsCl (Cesium Chloride) belongs to the fluorite structure. Assuming that $\mathrm{Cs}^{+}$ and $Cl^{-}$ ions are in contact along the cubic diagonal, and the ionic radius of $\mathrm{Cs}^{+}$ is 0.170 nm while the ionic radius of $Cl^{-}$ is 0.181 nm, calculate the packing density of the ions in the CsCl crystal structure is ().

Options:
A. 68.2%
B. 64.8%
C. 66.7%
D. 67.5%
E. 65.4%
F. 70.1%
G. 69.4%
H. 73.8%
I. 71.2%
J. 72.3%
Answer: A
Try to calculate and explain at what temperature the transition from extrinsic diffusion to intrinsic diffusion occurs in an MgO crystal containing $8 \times 10^{-9}$ of $\mathrm{Al_2O_3}$ impurities. If we want $\mathrm{Mg}^{2+}$ diffusion in MgO to remain extrinsic even up to MgO's melting point of 3000K (given that the formation energy of Schottky defects in MgO crystals is $6 \, \mathrm{eV} = 9.612 \times 10^{-19} \, \mathrm{J}$, $k = 1.380 \times 10^{-23} \, \mathrm{J/K}$), calculate the required concentration of $\mathrm{Al_2O_3}$ impurities is ().

Options:
A. $915.00K,1.15\times10^{-5}$
B. $760.30K,7.80\times10^{-6}$
C. $723.15K,7.50\times10^{-6}$
D. $812.50K,8.85\times10^{-6}$
E. $695.67K,6.45\times10^{-6}$
F. $845.12K,9.50\times10^{-6}$
G. $900.34K,1.05\times10^{-5}$
H. $870.22K,1.20\times10^{-5}$
I. $775.40K,8.23\times10^{-6}$
J. $835.77K,9.09\times10^{-6}$
Answer: J
When iron oxide FeO (NaCl-type structure) forms non-stoichiometric iron oxide in an oxidizing atmosphere, if the molar fraction of oxygen in the iron oxide is 52% and the lattice constant is 0.429 nm (given that the relative atomic masses of Fe and O are 55.8 and 16.0 respectively), calculate the ionic ratio of $\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}$ and its density is ().

Options:
A. 0.3,5.70g/cm³
B. 0.6,5.68g/cm³
C. 0.3,5.62g/cm³
D. 0.4,5.72g/cm³
E. 0.1,5.69g/cm³
F. 0.7,5.67g/cm³
G. 0.1,5.65g/cm³
H. 0.2,5.68g/cm³
I. 0.2,5.75g/cm³
J. 0.5,5.60g/cm³
Answer: H
The geostrophic wind is only directly proportional to ().

Options:
A. Centrifugal effect
B. Humidity levels
C. Temperature gradient
D. Magnetic field
E. Atmospheric pressure
F. Surface tension
G. Solar radiation
H. Turbulent flow
I. Potential gradient
J. Frictional force
Answer: I
Using the Saha equation, calculate the ratio of the number of H= ions to neutral hydrogen atoms in the Sun's photosphere is (). Take the temperature of the gas to be the effective temperature, and assume that the electron pressure is $1. 5 \, \mathrm{N} \, /\mathrm{m}^{-2}$ . Note that the Pauli exclusion principle requires that only one state can exist for the ion because its two electrons must have opposite spins.

Options:
A. $4\times10^{7}$
B. $6\times10^{8}$
C. $7\times10^{6}$
D. $5\times10^{8}$
E. $5\times10^{7}$
F. $3\times10^{7}$
G. $9\times10^{6}$
H. $2\times10^{7}$
I. $4\times10^{6}$
J. $1\times10^{8}$
Answer: E
Assume that the velocity of a CME directed toward Earth is 400 km $\mathrm{s}^{-1}$ and that the mass of the CME is $1 0^{1 3} \ \mathrm{k g}$
The kinetic energy contained in the CME, and compare your answer to the energy released in a large flare. Express your answer as a percentage of the energy of the flare is().

Options:
A. $$
K=6 \times1 0^{2 4} \mathrm{~ J}
$$
20%
B. $$
K=4 \times1 0^{2 2} \mathrm{~ J}
$$
6%
C. $$
K=9 \times1 0^{2 5} \mathrm{~ J}
$$
15%
D. $$
K=1 \times1 0^{2 4} \mathrm{~ J}
$$
12%
E. $$
K=2 \times1 0^{2 5} \mathrm{~ J}
$$
18%
F. $$
K=3 \times1 0^{2 3} \mathrm{~ J}
$$
11%
G. $$
K=7 \times1 0^{2 2} \mathrm{~ J}
$$
8%
H. $$
K=5 \times1 0^{2 2} \mathrm{~ J}
$$
5%
I. $$
K=8 \times1 0^{2 3} \mathrm{~ J}
$$
10%
J. $$
K=5 \times1 0^{2 4} \mathrm{~ J}
$$
22%
Answer: I
Using Kepler's laws, estimate the distance of the Moon from Earth at some time in the distant future when the Earth-Moon system is completely synchronized at 47 days.

Options:
A. $$
3. 8 \times1 0^{6} \mathrm{~ m}.
$$
B. $$
8. 5 \times1 0^{6} \mathrm{~ m}.
$$
C. $$
5. 5 \times1 0^{8} \mathrm{~ m}.
$$
D. $$
4. 4 \times1 0^{9} \mathrm{~ m}.
$$
E. $$
6. 1 \times1 0^{7} \mathrm{~ m}.
$$
F. $$
7. 0 \times1 0^{8} \mathrm{~ m}.
$$
G. $$
1. 2 \times1 0^{8} \mathrm{~ m}.
$$
H. $$
2. 5 \times1 0^{7} \mathrm{~ m}.
$$
I. $$
2. 2 \times1 0^{9} \mathrm{~ m}.
$$
J. $$
9. 9 \times1 0^{7} \mathrm{~ m}.
$$
Answer: C
The equation of hydrostatic equilibrium (Eq. 10.6), estimate the pressure at the center of Earth. Detailed computer simulations suggest that the central pressure is $3. 7 \times1 0^{6}$ atm is().

Options:
A. $$
3. 6 \times1 0^{6} \mathrm{~ a t m}
$$
B. $$
3. 8 \times1 0^{7} \mathrm{~ a t m}
$$
C. $$
5. 1 \times1 0^{6} \mathrm{~ a t m}
$$
D. $$
4. 2 \times1 0^{6} \mathrm{~ a t m}
$$
E. $$
3. 5 \times1 0^{4} \mathrm{~ a t m}
$$
F. $$
3. 9 \times1 0^{5} \mathrm{~ a t m}
$$
G. $$
3. 0 \times1 0^{5} \mathrm{~ a t m}
$$
H. $$
3. 3 \times1 0^{7} \mathrm{~ a t m}
$$
I. $$
4. 0 \times1 0^{6} \mathrm{~ a t m}
$$
J. $$
2. 5 \times1 0^{6} \mathrm{~ a t m}
$$
Answer: A
Suppose you lived on Mars and watched its moons. If Phobos and Deimos were next to each other one night, what would you see the next night (one Martian day later)? Describe the apparent motions of the two moons. (Both Phobos and Deimos orbit prograde, approximately above the planet's equator.)

Options:
A. Deimos is moving northward.
B. Deimos seems to pause momentarily.
C. Phobos is moving southward.
D. Deimos is moving eastward.
E. Phobos appears stationary.
F. Phobos is moving westward.
G. Phobos overtakes Deimos rapidly.
H. Phobos circles poleward quicker.
I. Deimos passes overhead slowly.
J. Deimos accelerates eastward fast.
Answer: F
Assume that a spherical dust grain located 1 AU from the Sun has a radius of 100 nm and a density of 3000 kg $\mathrm{m}^{-3}$ . In the absence of gravity, estimate the acceleration of that grain due to radiation pressure. Assume that the solar radiation is completely absorbed.

Options:
A. $$
0. 0 2 2 \, \mathrm{m \, s}^{-2}.
$$
B. $$
0. 0 5 0 \, \mathrm{m \, s}^{-2}.
$$
C. $$
0. 0 2 1 \, \mathrm{m \, s}^{-2}.
$$
D. $$
0. 0 1 5 \, \mathrm{m \, s}^{-2}.
$$
E. $$
0. 0 1 1 \, \mathrm{m \, s}^{-2}.
$$
F. $$
0. 0 0 9 \, \mathrm{m \, s}^{-2}.
$$
G. $$
0. 0 4 4 \, \mathrm{m \, s}^{-2}.
$$
H. $$
0. 0 3 3 \, \mathrm{m \, s}^{-2}.
$$
I. $$
0. 0 0 5 \, \mathrm{m \, s}^{-2}.
$$
J. $$
0. 1 0 0 \, \mathrm{m \, s}^{-2}.
$$
Answer: E
If the actual separation between HD 80606 and HD 80607 is 2000 AU, determine the orbital period of the binary star system. $H i n t$ : You may want to refer to the data in Appendix G to estimate the masses of the two stars.

Options:
A. $$
8 8, 0 0 0 \mathrm{~ y r}.
$$
B. $$
5 4, 0 0 0 \mathrm{~ y r}.
$$
C. $$
6 3, 0 0 0 \mathrm{~ y r}.
$$
D. $$
7 5, 0 0 0 \mathrm{~ y r}.
$$
E. $$
7 0, 0 0 0 \mathrm{~ y r}.
$$
F. $$
9 3, 0 0 0 \mathrm{~ y r}.
$$
G. $$
8 2, 0 0 0 \mathrm{~ y r}.
$$
H. $$
6 0, 0 0 0 \mathrm{~ y r}.
$$
I. $$
4 9, 5 0 0 \mathrm{~ y r}.
$$
J. $$
5 8, 0 0 0 \mathrm{~ y r}.
$$
Answer: C
The loss of the optical fiber is 0.5 dB/km at 1310 nm and 0.25 dB/km at 1550 nm. Suppose the following two optical signals enter the optical fiber simultaneously: a 150 $\mu\mathbf{W}$ optical signal with a wavelength of 1310 nm and a 100 $\mu\mathbf{W}$ optical signal with a wavelength of 1550 nm. What are the respective power levels of these two optical signals at 8 km and 20 km? Express the results in $\mu\mathbf{W}$.

Options:
A. $$
5 4 . 8 0 \ \mu\mathbf{W}
$$
$$
59.00 \ \mu\mathbf{W}
$$
$$
14\ \mu\mathbf{W}
$$
$$
30.00 \ \mu\mathbf{W}
$$
B. $$
6 0 . 0 0 \ \mu\mathbf{W}
$$
$$
64.10 \ \mu\mathbf{W}
$$
$$
15\ \mu\mathbf{W}
$$
$$
36.90 \ \mu\mathbf{W}
$$
C. $$
5 6 . 8 9 \ \mu\mathbf{W}
$$
$$
60.00 \ \mu\mathbf{W}
$$
$$
13\ \mu\mathbf{W}
$$
$$
35.00 \ \mu\mathbf{W}
$$
D. $$
5 9. 7 2 \ \mu\mathbf{W}
$$
$$
63.10 \ \mu\mathbf{W}
$$
$$
15\ \mu\mathbf{W}
$$
$$
31.62 \ \mu\mathbf{W}
$$
E. $$
5 5 . 2 6 \ \mu\mathbf{W}
$$
$$
60.10 \ \mu\mathbf{W}
$$
$$
19\ \mu\mathbf{W}
$$
$$
34.20 \ \mu\mathbf{W}
$$
F. $$
5 9 . 2 8 \ \mu\mathbf{W}
$$
$$
62.00 \ \mu\mathbf{W}
$$
$$
12\ \mu\mathbf{W}
$$
$$
30.10 \ \mu\mathbf{W}
$$
G. $$
5 8 . 5 5 \ \mu\mathbf{W}
$$
$$
63.50 \ \mu\mathbf{W}
$$
$$
13\ \mu\mathbf{W}
$$
$$
32.12 \ \mu\mathbf{W}
$$
H. $$
5 8 . 7 4 \ \mu\mathbf{W}
$$
$$
61.00 \ \mu\mathbf{W}
$$
$$
17\ \mu\mathbf{W}
$$
$$
28.98 \ \mu\mathbf{W}
$$
I. $$
5 7 . 0 0 \ \mu\mathbf{W}
$$
$$
61.50 \ \mu\mathbf{W}
$$
$$
18\ \mu\mathbf{W}
$$
$$
32.00 \ \mu\mathbf{W}
$$
J. $$
6 0 . 1 0 \ \mu\mathbf{W}
$$
$$
65.00 \ \mu\mathbf{W}
$$
$$
16\ \mu\mathbf{W}
$$
$$
33.20 \ \mu\mathbf{W}
$$
Answer: D
Given that the refractive index of the uniform optical fiber core is $n_{1} = 1.5$, the relative refractive index difference $\Delta = 0.01$, and the core radius $a = 25 \ \mu m$, calculate: if $\lambda_{0} = 1 \ \mu\mathrm{m}$, what are the normalized frequency $V$ of the optical fiber and the number of modes $M$ transmitted within it?

Options:
A. 32.50, 520
B. 36.00, 575
C. 33.32,555
D. 30.75, 525
E. 31.88, 540
F. 32.10, 580
G. 34.15, 590
H. 33.00, 510
I. 35.20, 560
J. 34.50, 530
Answer: C
The relative refractive index difference $\Delta\!=\! 0. \, 0 0 5 \,, \, \, n_{1} \!=\! 1. \, 5 0$ for a step-index optical fiber. When the wavelengths are 0.85 $\mu\mathrm{m}$, 1.3 $\mu\mathrm{m}$, and 1.55 $\mu\mathrm{m}$, what should the value of $a$ be to achieve single-mode transmission?

Options:
A. $$
a_{1} \leq2. 1 2 \ \mu\mathrm{m} \qquad a_{2} \leq3. 3 0 \ \mu\mathrm{m} \qquad a_{3} \leq3. 9 0 \ \mu\mathrm{m}
$$
B. $$
a_{1} \leq2. 2 0 \ \mu\mathrm{m} \qquad a_{2} \leq3. 4 5 \ \mu\mathrm{m} \qquad a_{3} \leq4. 0 5 \ \mu\mathrm{m}
$$
C. $$
a_{1} \leq1. 9 8 \ \mu\mathrm{m} \qquad a_{2} \leq3. 1 6 \ \mu\mathrm{m} \qquad a_{3} \leq3. 7 5 \ \mu\mathrm{m}
$$
D. $$
a_{1} \leq2. 0 2 \ \mu\mathrm{m} \qquad a_{2} \leq3. 2 0 \ \mu\mathrm{m} \qquad a_{3} \leq3. 7 8 \ \mu\mathrm{m}
$$
E. $$
a_{1} \leq2. 1 5 \ \mu\mathrm{m} \qquad a_{2} \leq3. 3 1 \ \mu\mathrm{m} \qquad a_{3} \leq3. 9 3 \ \mu\mathrm{m}
$$
F. $$
a_{1} \leq2. 1 7 \ \mu\mathrm{m} \qquad a_{2} \leq3. 3 2 \ \mu\mathrm{m} \qquad a_{3} \leq3. 9 6 \ \mu\mathrm{m}
$$
G. $$
a_{1} \leq2. 1 1 \ \mu\mathrm{m} \qquad a_{2} \leq3. 2 9 \ \mu\mathrm{m} \qquad a_{3} \leq3. 8 8 \ \mu\mathrm{m}
$$
H. $$
a_{1} \leq1. 8 5 \ \mu\mathrm{m} \qquad a_{2} \leq3. 0 8 \ \mu\mathrm{m} \qquad a_{3} \leq3. 6 5 \ \mu\mathrm{m}
$$
I. $$
a_{1} \leq2. 0 5 \ \mu\mathrm{m} \qquad a_{2} \leq3. 2 5 \ \mu\mathrm{m} \qquad a_{3} \leq3. 8 0 \ \mu\mathrm{m}
$$
J. $$
a_{1} \leq2. 0 8 \ \mu\mathrm{m} \qquad a_{2} \leq3. 2 7 \ \mu\mathrm{m} \qquad a_{3} \leq3. 8 2 \ \mu\mathrm{m}
$$
Answer: F
The energy of photons emitted by a semiconductor laser is approximately equal to the bandgap width of the material. Given that the $E_{\mathrm{g}}$ of GaAs material is $1.43~\mathrm{eV}$ and the $E_{\mathrm{g}}$ of a certain InGaAsP material is $0.96~\mathrm{eV}$, calculate their emission wavelengths ____.

Options:
A. $1.20 \mu\mathrm{m (GaAs material)},$
$0.92 \mu\mathrm{m (GaAs material)}$
B. $1.43 \mu\mathrm{m (GaAs material)},$
$0.87 \mu\mathrm{m (GaAs material)}$
C. $1.10 \mu\mathrm{m (GaAs material)},$
$0.96 \mu\mathrm{m (GaAs material)}$
D. $0.95 \mu\mathrm{m (GaAs material)},$
$1.5 \mu\mathrm{m (GaAs material)}$
E. $0.70 \mu\mathrm{m (GaAs material)},$
$1.0 \mu\mathrm{m (GaAs material)}$
F. $0.87 \mu\mathrm{m (GaAs material)},$
$1.3 \mu\mathrm{m (GaAs material)}$
G. $0.75 \mu\mathrm{m (GaAs material)},$
$1.5 \mu\mathrm{m (GaAs material)}$
H. $1.00 \mu\mathrm{m (GaAs material)},$
$1.4 \mu\mathrm{m (GaAs material)}$
I. $0.85 \mu\mathrm{m (GaAs material)},$
$1.6 \mu\mathrm{m (GaAs material)}$
J. $0.90 \mu\mathrm{m (GaAs material)},$
$1.2 \mu\mathrm{m (GaAs material)}$
Answer: F
A photodiode has a responsivity of $0.6 \ \mathrm{A/W}$ when $\lambda = 1.3 \ \mu m$. Calculate its quantum efficiency _____.

Options:
A. 0.561
B. 0.513
C. 0.635
D. 0.590
E. 0.482
F. 0.602
G. 0.547
H. 0.572
I. 0.598
J. 0.524
Answer: H
There is a step-index optical fiber, with the refractive indices of the core and cladding being $n_{1}=1.46, \, n_{2}=1.45$. Determine the values of $\mathrm{NA}, \ \theta_{\mathrm{max}}, \ \Delta T / L$, and $BL$ How many are they?

Options:
A. $$0.17$$
$$
9. 8^{\circ}
$$
$$
3 3. 2 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
3 0 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
B. $$0.13$$
$$
6. 8^{\circ}
$$
$$
2 9. 5 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
2 6 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
C. $$0.18$$
$$
9. 0^{\circ}
$$
$$
3 2. 0 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
3 1 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
D. $$0.20$$
$$
7. 9^{\circ}
$$
$$
3 0. 0 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
2 8 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
E. $$0.15$$
$$
8. 5^{\circ}
$$
$$
3 2. 5 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
2 5 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
F. $$0.21$$
$$
1 2. 1^{\circ}
$$
$$
3 5. 0 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
3 3 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
G. $$0.14$$
$$
7. 5^{\circ}
$$
$$
3 0. 8 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
2 9 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
H. $$0.22$$
$$
1 3. 0^{\circ}
$$
$$
3 6. 4 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
3 4 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
I. $$0.16$$
$$
1 0. 5^{\circ}
$$
$$
3 1. 6 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
3 6 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
J. $$0.19$$
$$
1 1. 2^{\circ}
$$
$$
3 4. 8 ~ \mathrm{n s} / \mathrm{k m}
$$
$$
3 5 \ \mathrm{M b} \cdot\mathrm{k m / s}
$$
Answer: A
The optical cable loss is 2 dB/km, the system's average connection loss is 1.5 dB/km, and the connection loss at the optical source and detector is 1 dB each. The system margin is 6 dB, the optical transmitter power is -13 dBm, and the optical receiver sensitivity is -42 dBm. Assuming the system is a loss-limited system, calculate the maximum unrepeated transmission distance as ____.

Options:
A. 3km
B. 9km
C. 5km
D. 11km
E. 6km
F. 4km
G. 10km
H. 8km
I. 2km
J. 7km
Answer: E
A system is designed to transmit 622 Mb/s via a 50 km cable with 0.4 dB/km attenuation. The system consists of two connectors with 1.5 dB loss, a laser source with 0 dBm power coupled into the fiber, and a receiver with a sensitivity of -34 dBm. If the system has a margin of 8dB, calculate how many connectors with an average power of 0.15 dB can be included in the system?

Options:
A. 24 (units)
B. 16 (units)
C. 28 (units)
D. 19 (units)
E. 25 (units)
F. 30 (units)
G. 15 (units)
H. 20 (units)
I. 18 (units)
J. 22 (units)
Answer: H
Assume that the optical gain $G(\lambda)$ of the laser satisfies the Gaussian relationship:
$$
G \left( \lambda \right) = G_{0} \mathrm{e}^{-(\lambda - \lambda_{0})^{2} / 2 \sigma^{2}}
$$
where the central wavelength is $\lambda_{0} = 0.85 \, \mu\mathrm{m}$, the gain spectral width is $\sigma = 32 \, \mathrm{nm}$, and the peak gain is $G_{0} = 5 \, \mathrm{mm}^{-1}$. If the resonator length of the laser is $0.35 \, \mathrm{mm}$, the refractive index of the material is $3.7$, and the total loss in the resonator is $\alpha_{r} = 3 \, \mathrm{mm}^{-1}$, determine how many longitudinal modes are excited in this laser system?

Options:
A. 299
B. 273
C. 284
D. 320
E. 288
F. 305
G. 277
H. 291
I. 315
J. 310
Answer: A
Due to the dispersion of the fiber, the Gaussian input optical pulse with variance of $\sigma_{1}$is broadened to the Gaussian output optical pulse with variance of $\sigma_{2} (\sigma_{2} >$$\sigma_{1})$. Try: optical frequency transfer function $| H (f) |$and $f_ {c}$____ on the relationship, where $f_ {c}$ is $|H(f) |$ 3 db bandwidth.

Options:
A. $$
H_{0} \mathrm{e}^{-( f / f_{c} )^{3} \mathrm{l n} 2}
$$
B. $$
H_{0} \mathrm{e}^{-( f / f_{c} )^{2.5} \mathrm{l n} 2}
$$
C. $$
H_{0} \mathrm{e}^{-( 2f / f_{c} )^{2} \mathrm{l n} 2}
$$
D. $$
H_{0} \mathrm{e}^{-( f / 2f_{c} )^{2} \mathrm{l n} 2}
$$
E. $$
H_{0} \mathrm{e}^{-( f / f_{c} )^{2} \mathrm{exp}( \mathrm{l n} 2)}
$$
F. $$
H_{0} \mathrm{e}^{-( f / f_{c} )^{2} \mathrm{l n} 3}
$$
G. $$
H_{0} \mathrm{e}^{-( f / f_{c} )^{2} \mathrm{l n} 2}
$$
H. $$
H_{0} \mathrm{e}^{-( f^{2} / f_{c} ) \mathrm{l n} 2}
$$
I. $$
H_{0} \mathrm{e}^{-( f / f_{c} )^{4} \mathrm{l n} 3}
$$
J. $$
H_{0} \mathrm{e}^{-( f / f_{c} )^{2} \mathrm{l n} 4}
$$
Answer: G
Given: (1) Si-PIN photodiode, quantum efficiency $\eta=0.7$, wavelength $\lambda=0.85 \, \mathrm{\mu m}$; (2) $Ge$ photodiode, $\eta=0.4$, $\lambda=1.6 \, \mathrm{\mu m}$. Calculate their responsivity $R$ as _____.

Options:
A. $$
0. 4 8 5 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 0 5 \mathrm{A} / \mathrm{W}
$$
B. $$
0. 4 6 5 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 2 0 \mathrm{A} / \mathrm{W}
$$
C. $$
0. 4 7 5 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 1 5 \mathrm{A} / \mathrm{W}
$$
D. $$
0. 4 8 0 \mathrm{A} / \mathrm{W}
$$
$$
0. 516 \mathrm{A} / \mathrm{W}
$$
E. $$
0. 4 6 0 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 3 5 \mathrm{A} / \mathrm{W}
$$
F. $$
0. 4 9 0 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 4 0 \mathrm{A} / \mathrm{W}
$$
G. $$
0. 4 3 0 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 3 0 \mathrm{A} / \mathrm{W}
$$
H. $$
0. 4 9 5 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 2 5 \mathrm{A} / \mathrm{W}
$$
I. $$
0. 4 4 0 \mathrm{A} / \mathrm{W}
$$
$$
0. 5 4 5 \mathrm{A} / \mathrm{W}
$$
J. $$
0. 5 0 0 \mathrm{A} / \mathrm{W}
$$
$$
0. 4 5 0 \mathrm{A} / \mathrm{W}
$$
Answer: D
The electric field intensity generated by an infinitely large uniformly charged plane with thickness $d$ and volume charge density $p$ in three spatial regions is ().

Options:
A. $$
{\rho \varepsilon_{0}} x \! \left( x \!+\! {\frac{d} {2}} \right)
$$
B. $$
{\frac{\rho x} {\varepsilon_{0} d}} \! \left( {\frac{x} {d}} \!-\! 1 \right)
$$
C. $$
{\frac{\rho} {\varepsilon_{0}}} \! \left( x \!+\! {\frac{d} {2}} \right)
$$
D. $$
{\frac{\rho d} {2 \varepsilon_{0}}} \! \left( 1 \!+\! x^2 \right)
$$
E. $$
{\frac{\varepsilon_{0}} {\rho}} \! \left( x \!-\! {\frac{d} {2}} \right)
$$
F. $$
{\frac{\rho x} {\varepsilon_{0}}} \! \left( {\frac {d} {2}} \!+\! x \right)
$$
G. $$
{\frac{\rho d} {2 \varepsilon_{0}}} \! \left( 1 \!-\! {\frac{x} {d}} \right)
$$
H. $$
\left( {\frac{\rho d} {\varepsilon_{0}}} \! \right) x \!-\! {\frac{d^2} {2}}
$$
I. $$
{\frac{\rho} {\varepsilon_{0}}} \! \left( x^2 \!-\! {\frac{d^2} {4}} \right)
$$
J. $$
{\frac{\rho} {\varepsilon_{0}}} \! \left( x \!-\! {\frac{d} {2}} \right)
$$
Answer: J
A cylinder of permanent magnet material with a radius of $a$ and a length of $2l$ is permanently magnetized to a magnetization intensity of $M_{0} e_{z}$. The magnetic induction $B$ and the magnetic field strength $H$ at any point on the axis is ().

Options:
A. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+\left( l-z \right)^{2}}}+\frac{l} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+( l-z )^{2}}}+\frac{l} {\sqrt{a^{2}+( l+z )^{2}}} ] e_{z}
$$
B. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+\left( l-z \right)^{2}}}+\frac{l+z} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+( l-z )^{2}}}+\frac{l+z} {\sqrt{a^{2}+( l+z )^{2}}}-2 ] e_{z}
$$
C. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{z} {\sqrt{a^{2}+\left( l-z \right)^{2}}}+\frac{l-z} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{z} {\sqrt{a^{2}+( l-z )^{2}}}-\frac{l-z} {\sqrt{a^{2}+( l+z )^{2}}} ] e_{z}
$$
D. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{l+z} {\sqrt{a^{2}+\left( l+z \right)^{2}}}-\frac{l} {\sqrt{a^{2}+\left( l-z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{l+z} {\sqrt{a^{2}+( l+z )^{2}}}+\frac{z} {\sqrt{a^{2}+( l-z )^{2}}} ] e_{z}
$$
E. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{l} {\sqrt{a^{2}+\left( l-z \right)^{2}}}-\frac{z} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{l} {\sqrt{a^{2}+( l-z )^{2}}}-\frac{z} {\sqrt{a^{2}+( l+z )^{2}}} ] e_{z}
$$
F. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+\left( l-z \right)^{2}}}+\frac{z} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+( l-z )^{2}}}-\frac{l+z} {\sqrt{a^{2}+( l+z )^{2}}} ] e_{z}
$$
G. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{l+z} {\sqrt{a^{2}+\left( l-z \right)^{2}}}+\frac{z-l} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{l+z} {\sqrt{a^{2}+( l-z )^{2}}}+\frac{z-l} {\sqrt{a^{2}+( l+z )^{2}}} ] e_{z}
$$
H. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+\left( l+z \right)^{2}}}-\frac{l+z} {\sqrt{a^{2}+\left( l-z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{l-z} {\sqrt{a^{2}+( l+z )^{2}}}-\frac{l+z} {\sqrt{a^{2}+( l-z )^{2}}} ] e_{z}
$$
I. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{z} {\sqrt{a^{2}+\left( l-z \right)^{2}}}+\frac{z+l} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{z} {\sqrt{a^{2}+( l-z )^{2}}}+\frac{z+l} {\sqrt{a^{2}+( l+z )^{2}}} ] e_{z}
$$
J. $$
B= \frac{\mu_{0} M_{0}} {2} [ \frac{z-l} {\sqrt{a^{2}+\left( l-z \right)^{2}}}+\frac{z+l} {\sqrt{a^{2}+\left( l+z \right)^{2}}} ] e_{z}
$$
$$
H=\frac{M_{0}} {2} [ \frac{z-l} {\sqrt{a^{2}+( l-z )^{2}}}+\frac{z+l} {\sqrt{a^{2}+( l+z )^{2}}} ] e_{z}
$$
Answer: B
Two coaxial thin metal cylinders, with radii $R_{1}=5 \, \mathrm{cm}$ and $R_{2}=6 \, \mathrm{cm}$, respectively, have a smaller cylinder of length $l=1 \, \mathrm{m}$ placed inside the larger cylinder. The dielectric constant of the material between the plates is $\varepsilon_{0}$. If a voltage of $U=1000 \, \mathrm{V}$ is applied between the two cylinders, what is the electrostatic energy stored between the plates of the capacitor?

Options:
A. $1.57\times10^{-7}$
B. $1.49\times10^{-7}$
C. $1.45\times10^{-7}$
D. $1.60\times10^{-7}$
E. $1.52\times10^{-7}$
F. $1.50\times10^{-7}$
G. $1.65\times10^{-7}$
H. $1.58\times10^{-7}$
I. $1.48\times10^{-7}$
J. $1.55\times10^{-7}$
Answer: E
Assume there is a plane electromagnetic wave in the air where the electric field intensity at the origin is given by $E=E_{x} ( 0, t )=E_{\mathrm{m}} \cos \omega t$, and the electromagnetic wave propagates along the $z$-axis at a speed of $\nu$. What are the expressions for the electric field intensity and magnetic field intensity?

Options:
A. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{sin} \omega{\biggl(} t+{\frac{z} {\nu}} {\biggr)} e_{z}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} \varepsilon_{0}}}} \operatorname{sin} \omega\biggl( t+{\frac{z} {\nu}} \biggr) e_{x}
$$
B. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{c o s} \omega{\biggl(} t-{\frac{z} {c}} {\biggr)} e_{x}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} \cdot \varepsilon_{0}}}} \operatorname{sin} \omega\biggl( t-{\frac{z} {c}} \biggr) e_{y}
$$
C. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{c o s} \omega{\biggl(} t-{\frac{z} {c}} {\biggr)} e_{x}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\varepsilon_{0} / \mu_{0}}}} \operatorname{c o s} \omega\biggl( t-{\frac{z} {c}} \biggr) e_{y}
$$
D. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{c o s} \omega{\biggl(} t+{\frac{z} {\nu}} {\biggr)} e_{x}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} / \varepsilon_{0}}}} \operatorname{c o s} \omega\biggl( t+{\frac{z} {\nu}} \biggr) e_{y}
$$
E. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{c o s} \omega{\biggl(} t-{\frac{z} {\nu}} {\biggr)} e_{x}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} / \varepsilon_{0}}}} \operatorname{c o s} \omega\biggl( t-{\frac{z} {\nu}} \biggr) e_{y}
$$
F. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{sin} \omega{\biggl(} t-{\frac{z} {\nu}} {\biggr)} e_{x}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\mu_{0}}} \operatorname{c o s} \omega\biggl( t-{\frac{z} {\nu}} \biggr) e_{y}
$$
G. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{c o s} \omega{\biggl(} t-{\frac{z} {\nu}} {\biggr)} e_{z}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} \varepsilon_{0}}}} \operatorname{c o s} \omega\biggl( t-{\frac{z} {\nu}} \biggr) e_{x}
$$
H. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{sin} \omega{\biggl(} t+{\frac{z} {\nu}} {\biggr)} e_{x}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} \cdot \varepsilon_{0}}}} \operatorname{sin} \omega\biggl( t+{\frac{z} {\nu}} \biggr) e_{y}
$$
I. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{sin} \omega{\biggl(} t-{\frac{z} {\nu}} {\biggr)} e_{x}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} \cdot \varepsilon_{0}}}} \operatorname{sin} \omega\biggl( t-{\frac{z} {\nu}} \biggr) e_{y}
$$
J. $$E {\bigl(} z, t {\bigr)}=E_{m} \operatorname{c o s} \omega{\biggl(} t-{\frac{z} {\nu}} {\biggr)} e_{y}$$
$$
H\bigl( z, t \bigr)={\frac{E_{m}} {\sqrt{\mu_{0} / \varepsilon_{0}}}} \operatorname{c o s} \omega\biggl( t-{\frac{z} {\nu}} \biggr) e_{z}
$$
Answer: E
The magnetic permeability of a certain conductive medium is $\mu_{0}$, and its conductivity is $4.2 \ \mathrm{S/m}$. What is the frequency of an electromagnetic wave with a penetration depth of 1 meter?

Options:
A. $$
6. 0 3 \times1 0^{4} \, \mathrm{H z}
$$
B. $$
4. 8 4 \times1 0^{4} \, \mathrm{H z}
$$
C. $$
7. 4 6 \times1 0^{4} \, \mathrm{H z}
$$
D. $$
2. 6 7 \times1 0^{4} \, \mathrm{H z}
$$
E. $$
1. 5 0 \times1 0^{4} \, \mathrm{H z}
$$
F. $$
5. 0 1 \times1 0^{4} \, \mathrm{H z}
$$
G. $$
9. 3 1 \times1 0^{4} \, \mathrm{H z}
$$
H. $$
7. 9 2 \times1 0^{4} \, \mathrm{H z}
$$
I. $$
3. 9 9 \times1 0^{4} \, \mathrm{H z}
$$
J. $$
8. 2 5 \times1 0^{4} \, \mathrm{H z}
$$
Answer: A
In an infinite, uniform dielectric with a conductivity of $\sigma$, there are two ideal conductive spheres with radii $R_{1}$ and $R_{2}$, separated by a distance $d \left( d \gg R_{1}, d \gg R_{2} \right)$. Find the resistance between the surfaces of the two conductive spheres.

Options:
A. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}}-\frac{1} {R_{2}^{2}}+\frac{1} {d \,-\, R_{1}^{2}}-\frac{1} {d^{2} \,-\, R_{2}} \Big)
$$
B. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}}+\frac{1} {R_{2}}-\frac{1} {d \,-\, R_{1}}-\frac{1} {d \,-\, R_{2}} \Big)
$$
C. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}}+\frac{1} {R_{2}}-\frac{1} {d^{2} \,+\, R_{1}}-\frac{1} {d^{2} \,+\, R_{2}} \Big)
$$
D. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}}+\frac{1} {R_{2}}+\frac{1} {d \,+\, R_{1}}+\frac{1} {d \,+\, R_{2}} \Big)
$$
E. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}^{3}}+\frac{1} {R_{2}^{3}}-\frac{1} {d \,+\, R_{1}}-\frac{1} {d \,+\, R_{2}} \Big)
$$
F. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}}+\frac{1} {R_{2}}+\frac{1} {d^{3} \,-\, R_{1}}+\frac{1} {d^{3} \,-\, R_{2}} \Big)
$$
G. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}}-\frac{1} {R_{2}}-\frac{1} {d \,+\, R_{1}}+\frac{1} {d \,-\, R_{2}} \Big)
$$
H. $$
= \frac{1} {4 \, \pi\sigma} \Big( \frac{1} {R_{1}^{2}}+\frac{1} {R_{2}^{2}}-\frac{1} {d^{2} \,-\, R_{1}}-\frac{1} {d^{2} \,-\, R_{2}} \Big)
$$
I. $$
= \frac{1} {4 \, \pi\sigma} \Big( \ln{R_{1}}+\ln{R_{2}}+\ln{(d \,+\, R_{1})}+\ln{(d \,+\, R_{2})} \Big)
$$
J. $$
= \frac{1} {4 \, \pi\sigma} \Big( \ln{R_{1}}+\ln{R_{2}}-\ln{(d \,-\, R_{1})}-\ln{(d \,-\, R_{2})} \Big)
$$
Answer: B
The sinusoidal uniform plane wave with a frequency of $f=500$ kHz propagates in an ideal medium, with the electric field amplitude vector $E_{\mathrm{m}} = e_{\mathrm{x}} 4 - e_{\mathrm{y}} + e_{\mathrm{z}} 2 \, \mathrm{kV/m}$ and the magnetic field amplitude vector $H_{\mathrm{m}} = e_{\mathrm{x}} 6 + e_{\mathrm{y}} 18 - e_{\mathrm{z}} 3 \, \mathrm{A/m}$. Find the unit vector in the direction of wave propagation.

Options:
A. $$
=-\ e_{x} 0. 3 7 5 \,+\, e_{y} 0. 2 7 3 \,+\, e_{z} 0.
$$
B. $$
=-\ e_{x} 0. 6 4 8 \,+\, e_{y} 0. 2 8 5 \,+\, e_{z} 0.
$$
C. $$
=-\ e_{x} 0. 1 2 5 \,+\, e_{y} 0. 3 9 8 \,+\, e_{z} 0.
$$
D. $$
=-\ e_{x} 0. 4 7 2 \,+\, e_{y} 0. 3 7 0 \,+\, e_{z} 0.
$$
E. $$
=-\ e_{x} 0. 2 5 0 \,+\, e_{y} 0. 1 5 3 \,+\, e_{z} 0.
$$
F. $$
=-\ e_{x} 0. 7 2 1 \,+\, e_{y} 0. 4 0 5 \,+\, e_{z} 0.
$$
G. $$
=-\ e_{x} 0. 2 8 7 \,+\, e_{y} 0. 6 3 0 \,+\, e_{z} 0.
$$
H. $$
=-\ e_{x} 0. 0 6 2 \,+\, e_{y} 0. 5 2 4 \,+\, e_{z} 0.
$$
I. $$
=-\ e_{x} 0. 5 0 0 \,+\, e_{y} 0. 3 4 0 \,+\, e_{z} 0.
$$
J. $$
=-\ e_{x} 0. 8 5 0 \,+\, e_{y} 0. 4 1 0 \,+\, e_{z} 0.
$$
Answer: A